Yeah, I think that those "Zotac GT730 GDDR5 1GB" versions are still floating around in various channels, Altatac is selling them on ebay and Newegg Marketplace. I bought five of them (refurb), when I put two into a cruncher, they were crashing hard, but the other three, crunched just fine in my other quad-GPU mobo/rig. And yet, an RX 460 and RX 570 are crunching away in the first PC. So I don't know what the issue was, other than maybe bad card.
I paid $40 ea., haven't tried any games on them (they are only 1GB, but GDDR5), found a YT vid of one of these cards supposedly playing GTA V. I guess they can play it, with appropriate settings.
Edit: But those Zotac cards aren't Low-Profile. Again, I guess not a contender.
I think that there does exist a LP GT730 GDDR5 card, but it may be hard to find these days.
Sorry, OP, your price range doesn't leave much.
A LP GT710 is like $30-50, and a LP GT1030 2GB GDDR5 is like $85-120.