No worries at all! So your issue is two fold.
First, that is a JL wheel which has 6.25” factory backspacing. Factory TJ wheels have 5.25” backspacing. That means your JL wheel is sitting 1” closer to the vehicle than a factory TJ wheel, hence the reason it’s contacting things.
In addition, that is a much wider tire than a stock TJ tire size, so it’s causing things to contact even more.
To get that spare tire to mount, you’ll need to put at least a 1” wheel spacer on the spare tire mount, then mount the spare to that. I would say 1.5” spacer would be ideal.
However, that larger tire and the extra leverage from the spacer is going to destroy your tailgate in short order.
You really want to solve this by getting an Exogate / MORryde heavy duty tire carrier. They are priced well and will solve your issue, along with a wheel spacer as well.