I've had this issue with a couple XJs (2000 - 2001) and 3 TJs, all '03 and up. I too toyed with the idea of hood vents, but didn't want to cut the hood, unless it was necessary. On the current TJ, I was having the same issue late this spring when it was warm. Jump in the Jeep, run into the convenience store, come out and start the Jeep, it stumbles. I added the Design Engineering kit in late May, then didn't have a single stumble all Summer (It was a hot one too).
https://www.amazon.com/dp/B015NOKWQY/?tag=wranglerorg-20
View attachment 283241
FWIW, there is a cheaper kit (I bought both to test them) that is 1/2 the cost. It is of course made in China and the quality is no where near as good as the Design engineering version.
https://www.amazon.com/gp/product/B08TTT8GVM/?tag=wranglerorg-20