My main system is running an AsRock 890GX Pro 3 with an AMD AM3 processor -- an 840-something quadcore.  It's about six years old now, I suppose, but I tell you what, I've enjoyed this mobo/processor combination like no other in recent memory. It is still a very fast machine, but I would just like to have a bit more (read a LOT more) horsepower, and I'd like to see if I can squeeze out a little more pop from the mobo before I have to retire it. Tell ya what, my next mobo is almost certainly gonna be an AsRock -- I like this one that much.

I've read where 890 GX Pro 3 will accept AM3+ processors and I see that there are some pretty fast AM3+ processors out there. But when I went to AsRock's website to check on which ones actually will work with my mobo, the list was for several older AM3+ processors, none of which are in production anymore. 

So I have a real simple question: what is the likelihood that a newer and faster AM3+ processor will work in this old board of mine, even though it is not specifically listed in the compatibility charts? I know, for example, that with other 'puter related items, just because something isn't shown as being compatible doesn't mean it won't work. And I guess I'm kinda wondering if this can hold true for processors as well.

Whatever CPU you pick, make sure it is on your supported CPU list and that you have your BIOS up to date before installing it 

This machine isn't used for gaming, btw. It is a DAW, a Digital Audio Workstation. I use it for recording and producing music. There are a couple of pieces of software I run that really put a load on the processor though, which is why I've been thinking about an upgrade.

So you guys think an X6 would be a better way to go than an X8?

a. Hard to find

b. The least powerful variants of the FX range

c. Run very hot and could damage your board/system (true of all FX 8 cores)

They may have a little more CPU grunt (2 extra cores) but it isn't worth the risk of damage, on top of that they are not "full" cores. It is broken up into 4 modules, each with 2 cores and 1 FPU (Math coprocessor). With audio applications your performance would be crippled by the shared FPUs, in essence making performance little better than a quad core with FPUs for each core.

The Phenom II x6s can be had on the cheap used and will be a huge upgrade over an old quad core Athlon II. Then you can save the little bit extra over the FX and put it toward a Ryzen 5 1600 or Ryzen 7 1700 system later on. Either of these would be ideal for your usage scenario with the 1700 being the best but the 1600 coming in cheaper albeit with 2 less cores. Both CPUs are hyperthreaded so you would get 12 threads on the 1600 and 16 threads on the 1700.