The RX6400 seems to be the best fit in this scenario that still comes with some unavoidable compatibility tradeoffs but that's just my 2c.
- The 16x slot is pretty close to the PSU so there might not be nice room for airflow there but could be manageable with a well placed fan.
- Are we sure that 4x slot is PCIe 3.x (it might be a 2.x slot)? If not you end up taking more of a hit to performance making the cost/perf less desirable even if it is still better than the iGPU.
The time a cost of modding that A2000 (which is pretty interesting) might as well buy a new PC. In that way at least even if the parts are somewhat at the lower end you can use them at their full potential.
Reusing the CPU and RAM could be an option with some good eBay finds on cases, motherboards, cooler, and PSU but still that cost might not be desirable if the OP only has a budget for a low tier GPU.