Re: SMD soldering. It's pretty easy if you get the technique down. Check out this pdf as an example from sparkfun http://www.sparkfun.com/datasheets/Prot Basics.pdf ... also this page has a lot more if you scroll down: http://www.sparkfun.com/commerce/tutori als_id=107
Thanks for the links! I have ordered non-SMD replacements though, so only the desoldering should be tricky.
You may want to check your power supply or the audio circuit with a multimeter. It's possible that your supply "works" but fucks up the audio. This was an issue with my first amiga and didn't really think of it until you said the caps were clean. There's a simple way to test for this/should be some instructions on aminet.
Interesting! The PSU I'm using is actually some very sketchy DIY thing the previous owner of my Amiga made. It may very well be the problem! I'll look into this, and if it is the problem, then I guess I'll just have the replacement caps ready for the future when they really do fail.