Switching to a six-core FX would be little more than a sidegrade, but going to an 8320 or 8350 will give you a big performance boost.
I had a 1035T for a long time and ran it at 3.6, then upgraded to an 8350 on the same board. At stock, the 8350 was just ahead of the overclocked Thuban, except in multi-core aware applications, where it won easily. But when I overclocked the 8350, it was clearly an improvement. It reached 4.5 GHz at stock voltage and is stable at 4.85 with 1.48v. Even at 4.5, it's clearly faster than the 1035T at 3.6 was, by at least 20 percent and often more than that.
Your motherboard will handle the 83x0 with no problem. I've been running on the 970 version of that board, the 970A-UD3, for well over a year with no issues.
I won't recommend the AMD 9-series chipset platform and FX to anyone buying from scratch, because it's a dead end and there are better ways to spend your money. But if you're already invested in AM3+, then the 83x0 processors still make very good sense as upgrades.
