My point is that you can get very nearly the same effect with an Instant:
Instant "If target creature dies this turn, target player discards three cards."
Instant "Regenerate target creature. If it regenerates this turn, put three +1/+1 counters on it."

If you're set on having a lasting effect, you can give a single-sided aura flash:
Flash Aura "Whenever ~ deals combat damage to a player, draw a card." (Ophidian Eye)

The Morph-Aura is very similar; the main difference being that you have to commit to which creature you're going to target before you'd like to otherwise. Is that something worth fighting for?

Strength Rune 3G
enchantment - aura
Enchant creature
enchanted creature gets +3/+3
Inscribe G, 4 (X: exile this face down from your hand with X charge counters. While it's exiled, it has, "G, remove 4 charge counters: put this onto the battlefield attached to target creature")

Flight Rune 1U
enchantment - aura
Enchant creature
enchanted creature gets +1/+1 and has flying
Inscribe U, 2 (X: exile this face down from your hand with X charge counters. While it's exiled it has, "U, remove 2 charge counters: put this onto the battlefield attached to target creature")

A lot of Runes in fantasy art tend to involve mages generating glowing magical runes that float in the air, and either flinging them or imbuing themselves with them. They're not necessarily carved on some surface.

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A creature protected with a circle of glowing runes.

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A guy projecting glyphs.

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Imagine if the art above had glyphs in the shapes of Eyes, Ankhs, or Scarabs. It could work as a fantasy concept.

Links to some more art:

Another guy projecting runes.

A guy with a rune carved on his face

A rune that's generating a force-field

Sometimes a magical rune can be a setup for casting a powerful spell. Here's another one. It's not exactly what I have in mind with the trap-runes, but they're glowing magical runes that look like they're generated on the spot, not necessarily things you carve in stone like real runes.

A simple search of digital art on DeviantArt with the keyword "rune"

Havelock's comment was questioning why traps have to be hieroglyphs, since hieroglyphs are carved on stone, not creatures.

I think the set should definitely have booby traps of some sort to represent the tomb raiding association with Egypt in pop culture. Since the word "Trap" have been used before, we need another name. We could also redo the Traps from Zendikar, but I really like the type of traps that you set in advance and watch people walk into.

A separate concern is that I want hieroglyphs to be in the set somewhere, and I don't think something hyper-literal such as enchanting walls is that fun. I put these two motives together to propose hieroglyphs as traps.

Traps and Hieroglyphs don't absolutely need to be bound together, but I don't see why the flavor can't work either.
These can be magical glyphs. The art can show these blue, shining symbols of Eyes or Ankhs glowing on people's foreheads or shoulders. We can give these symbols their own names, like "Magoglyph" with names like "Magoglyph of Sight" "Magoglyph of Retribution."

I don't think it's a stretch, considering other fantasy concepts that have sprung from real-life mundane counterparts. There's things like staffs, potions, scrolls, which have real-life uses but do something different in fantasy. The best example for this case might be Runic magic, which appears in lots of fantasy games. Real runes are carved on wood or stone. But fantasy rune-mages can project runes or imbue runes onto other things to grant some magical effect. In the Kamigawa novels, the main character is this Kanji mage who pulls off all sorts of tricks by inscribing Kanji letters with magcial properties onto things, including himself or other people. The same thing could work with magical glyphs.

Imagine that you play a face-up aura that says "whenever this creature deals combat damage to a player, draw a card" on your creature. Your opponent would insta-block it, or kill it if s/he has removal. But if it's face down, as far as your opponent knows it could be an aura that says "when this creature dies, target player discards 3 cards?" or "G: Regenerate this creature." Then the choice is not so easy and your opponent will have to guess your motive.

These cards can also be used for bluffing. You could put an irrelevant Aura on an opponent's creature face down and make the opponent scared to attack or block with it.

Another thing that the hidden info accomplishes is that it allows certain effects to actually trigger. For example, imagine that an Aura said, "whenever this creature would be dealt combat damage, regenerate it and put three +1/+1 counters on them." That just means no one would ever attack into it or block it, and you don't get the satisfaction of seeing it happen. In the words of Zac Hill, "those cards are lies and I hate them." But if the enchantment's text is hidden, you get to see it actually happen. So it's not just an Aura that you have to select a target in advance before casting them.

These hieroglyphs allow you to set up a trap and create a suspenseful, psychological guessing game. It adds a new angle to the game. That's what expansion sets need to do, and it's worth putting in some complexity points.

Morph could work too. As I understand it, they tried something like this with morph when designing traps in Zendikar. However, the rules were already defined that a face-down card on the battlefield is a 2/2 creature. I wonder if the rules can be changed to say that face-down cards that are attached to something are Aura cards with Enchant Permanent. But rules issues aside, I think it makes it easier to visually understand how the card works if it's printed on both sides. I'm not sure if morph can be done under the new world order. DFCs like werewolves have even more total text than morph, but they were doable under the new world order because the information is chunked into two sides.
— Chah

DFCs may be the way to go regardless, but there's no reason they have to be in play while face down, and the whole sharing a name thing is a big issue. Exile cards face down "marking" permanents, then put them onto the battlefield face up enchanting those permanent. In the trap vein, there's some discussion to be had over whether these want both trigger and condition as the card they turn into or whether the trigger should be what lets you turn them over. i.e.

Version 1:
Glyph of Permanence 3G
Enchantment - Aura Glyph
Enchant Permanent
Reveal GG (You may pay 2 to exile this card face down marking target permanent. Any time you could cast an instant you may pay its Reveal cost to put it onto the battlefield enchanting the marked permanent.)
If enchanted permanent would be destroyed, regenerate it.

Version 2:
Glyph of Permanence 3G
Enchantment - Aura Glyph
Enchant Permanent
Inscribe (You may pay 2 to exile this card face down marking target permanent.)
If marked permanent would be destroyed, you may pay GG. If you do, put ~ onto the battlefield enchanting it.
Enchanted Permanent is Indestructible.

Though given the need for replacement effects these will likely work better as Chah proposed them.
-Jules

Back side:

Mysterious Hieroglyphs 2
Enchantment - Aura Glyph
Enchant permanent
Activate (Pay this card's Glyph cost: Transform this card. )

Front side:

Glyph of Painful Retribution 1R
Enchantment - Aura Glyph
Enchant permanent
When enchanted permanent is put into a graveyard, ~ deals 5 damage to target player.
Glyph cost R

Another card:

(The Back side is the same):

Mysterious Hieroglyphs 2
Enchantment - Aura Glyph
Enchant permanent
Activate (Pay this card's Glyph cost: Transform this card. )

Front side:

Glyph of Revelations 2U
Enchantment - Aura Glyph
Enchant permanent
Whenever enchanted permanent deals combat damage to you or an opponent, you draw a card.
Glyph cost 1U

So it's like setting a trap on a permanent, and your opponent doesn't know what to expect.