Yikes, this thread went pretty crazy. But TBH, I think several of the suggestions are overkill. You've got a decent system already, plenty of ram too, no need to replace it all.
If I may, I'd suggest the following:
#1) get yourself an i7-47xx cpu, others with more knowledge in Intel stuff can be more detailed, but in short it should fit your board just fine and double your thread count (4t to 8t)
#2) Get yourself a used gpu with lotsa CUDA cores. You can find 970s for under 200 easily. Possibly 1050/1060s for 200-300$.
#3) (the weird one) I saw your board has some some slots on it? I didn't see which board you have, but regardless, you may want to consider this: grab a PCIe to nvme adapter and a modern nvme SSD. Doesn't have to be massive, you want it for speed. Yes yes, I know you've got SSDs galore already, but they're all limited by sata restrictions. A nvme SSD running directly from one of the PCIe slots will go at least 2-3x faster than your fastest Sara SSD, which will also help with your applications.
#3a) Alternative: if you can move some data around you can get more speed from those SSDs by putting two or more into a raid 0. Not as fast as the nvme option, but it'll cost Nadda.
Either way, all three options together shouldn't even hit the low end of your 600$ budget. Hope it helps.