You are still using sources outside the books regardless of why... anyway here's how I'd resolve it in 5e...
In 5e I'd rule it like this... Arcana skill check, hard DC (My Far North campaign is gritty, especially with regards to the use of magic otherwise I'd use medium or even an easy DC depending upon how easy or hard magic is to modify in the campaign world) ... so 6th level wizard with proficiency and let's say 18 INT... +4 Ability/+3 Prof= +7 vs. 20...35% chance (or if in a less gritty setting 65% for the DC 15... 85% for DC10, if there's no chance for failure why not just give the wizard a new spell??). The wizards spell Save DC is 15 and attack bonus is +7 which puts him in the dangerous category for traps... so let's say 4d10 at his level. Another way to adjudicate the damage would be to look at the improv table... more damage than hot coals but not as damaging as a lava stream... again 4d10. Dex save for half damage to anyone who gets caught by or enters the rug area. the effect lasts for 1d4 rounds. This actually seems pretty on point when compared with the fireball spell... slightly lower damage but with a chance for a slightly longer duration... Now how would anything in 4e have made this easier?
EDIT: Summary
Arcana: check DC 20 (though variable depending on the feel of magic in the camapign)
Damage: 4d10
Duration: 1d4 rounds
Save: Dex for half damage for anyone starting their turn on or entering the rug area
I was going to go with the exact same setup:
+ 3 Prof, + 4 Int = + 7 Arcana.
However, I was going to go with:
1) Medium DC 15 = 35 % chance to waste your Action by attempting the stunt.
2) 3d10 damage (I would put it somewhere between falling into a firepit and an outright cave-in so between 2d10 and 4d10)
4) This is a save versus an environmental effect, not save vs spell. Therefore the environmental DCs should apply. I would give the player the DC 12 (low end of Dangerous) even though it is halfway between Setback and Dangerous. The save would be Dex as you have. The Dex save for level 6 would run the gamut from + 1 to probably + 5ish. Let us just call it + 3. So we have the 35 % failure at the ability check level compounded by another ~ 55 % chance for failure at the save level.
5) If they're an Evoker (Scult Spell @ level 6), I'd give them 1/2 damage on a successful save.
6) What to do about AoE and duration? What are the mechanical concerns on this? Where is the guidance? With respect to the fiction, the burning rug should be an AoE, but there has to be balance constraints here. With respect to duration, 1d4 rounds seems reasonable enough. I see that in a few hazards and traps here and there. Sure, let us go with that. But 1d4 of what? What is the residual burn damage? Surely not 3d10 again!
Really what I'm looking to accomplish is:
(a) something cool and thematic
(b) something that is powerful enough and of which the player can reasonably expect to accomplish it such that it achieves reasonable parity with an alternative action, from a cost-benefit analysis perspective, thereby creating a legitimate decision-point for the player.
If there isn't reasonable parity, or reasonable potential return from a cost-benefit analysis perspective, then the stunting system is useless for actual play because pushing the reliable basic attack or spell button will always win out over the stunt option. If the stunting system is too powerful then the decision-point for the player is muted (or outright goes away). It is a fine line to walk.
If the Evoker player is facing the prospect of Firebolting (2d10 on single target, + 7 hit) or a more powerful limited use spell (eg Fireball @ 8d6, 20 ft radius, save 1/2, DC 15) vs an outright 35 % loss of the Action and a subsequent 55 % chance of failure (but save 1/2) @ 3d10 damage, DC 12, save 1/2, on maybe a 5 ft radius AoE (or maybe 10 ft?...how do I sort out the standardized radius for such a stunt)...do they go with the stunt or do they say EFF IT FIREBOLT/FIREBALL? I don't know. And even if I feel comfortable, and the table agrees with me, on the Ability Check DC, the Setback/Dangerous/Deadly qualification (and the picking out the DC # within that 2 to 4 number spread) there are variables in adjucation that are still difficult for me to sort out. AoE? If so, does that eat into the total damage budget of the effect? How big is standardized AoE or that achieves parity with an of-level effect? Duration or other effects? If I go 1d4 round duration, how much burn damage for entering the hazard or being there at the beginning (or end?) of your turn?
What I do know is that the procedure for the Arcana > Fire stunt in 4e is quick, requires minimal mental overhead on my part, minimal table handling time and achieves an interesting effect that results in relative parity (from a math and effects perspective) with an encounter power of that tier, thus attaining consistent relevance and resulting in a player decision-point.
EDIT - Oh and 5e is not remotely even in the same universe as Rules-Lite. Not even close. For the highest threshold of a Rules-Lite qualification, I would with the Powered by the Apocalypse systems. Core, simple, unified resolution mechanics that are applied in all situations and achieve interesting outcomes that properly model genre/tropes and achieve play agenda. They don't require GM force or an abundance of rulings and/or referencing of rules/charts. You just apply straight-forward, transparent play procedures and the system's inertia and proficient GMing/playing will spin out a rewarding experience. 5e has tons of intersecting resolution mechanics, PC build schemes, massive spell lists, etc. Not Rules-Lite.