If you were watching something like Task Manager's CPU monitor as Overall Utilization, you might not see how much an operation actually depends on the CPU.
If you switch the view to "Logical Processors", you'll see how much Spine actually hits your CPU as single thread when exporting PNGs.
Rendering is done by GPU (pretty much the same way how it renders things in the Spine viewport), but PNG compression is done on the CPU.
Highly-compressed PNGs can take a really long time but, depending on the image, the compression can mean a big difference in file size.
Spine 3.6 doesn't let you choose the compression level but a bunch of new export settings have been added in 3.7. This includes compression level.
With 3.7, you can probably do it this way:
- Export PNG sequences at the lowest compression level.
- Run your exported files through a free PNG compressor at a later time if you need them to be smaller. (eg, On Windows, PNGGauntlet works for this purpose. You can run it multi-threaded to compress multiple files at a time, or run it single-threaded so you can still use your computer while it runs in the background. Sadly doesn't have any middle options.)
As for getting a new GPU, if you're not experiencing slowdown in the viewport, buying a new graphics card probably won't make much of a difference for PNG export.