I am not an amp tech, nor do I play one on TV.
However, as a computer tech, I have a load of experience re-capping system boards.
Electrolytics do indeed dry out and go South permanently.
Visually, you can look for leakage and bulged tops.
The ESR meter will confirm you have a bad cap, but often you have to remove it to check out of circuit.
At that point, it gets replaced anyway.
The caps most subject to damage are those that run the hottest.
Higher voltage, or caps subject to lots of ripple filtering are high on the list.
To do a decent job, you will require a soldering station with an adjustable range up to 450C.
You want to heat the local area quickly without heating up the surrounding area.
A desoldering station, with vacuum assist makes for the cleanest job.
There is a learning curve as you come up to speed.
These are not investments one makes for a one-off repair.
If you can find somebody competent at recapping, it is probably more cost effective to hire them.
I use Panasonic when I cannot get Rubycon.
A domestic supplier for Rubycon and other premium caps is The Cap King