You seem to be adamant about trying this, so lets dance. I like experiments. I should also say that none of this is guaranteed to work, nor to work well enough for a good gaming experience. But I'll try to give you the best shot at success instead of wasting money on things that are guaranteed NOT to work.
What country do you live in?
Throwing out GPU names doesn't mean much. A new/current gen GPU will be your best bet from a performance/power efficiency standpoint.
As I said previously, since you're working with closed-ended PCIex1 slots that are only rated for 10W, you'll need a PCIe riser, similar to what crypto miners use (
Here's an example). Because of that, you're going to need a "low-profile" GPU in order to get it mounted to the back of the case. This is assuming your case isn't so narrow as to require a low profile card already. If that's the case, we're in trouble.
Also, please provide the width (side to side across the back face) of the case.