First of all, I think you shouldn't "try" to listen to the differences that may happen (or not) when you change something. Particularly when you can't swap parts quickly to check on that..
Try not to "imagine" or "think" on what has changed. Dramatic changes may happen, but they are rare. Sometimes it means distortion increase, which is the opposite of what you should look for.
Just plain listening, and see if you enjoy it and can listen for a long time, without irritations.
My advice is to pay attention to the separation of the instruments, the wideness and deepness of the stage, the small harmonics that come or go with the change. Stage deepness is difficult or impossible to evaluate with headphones though.
This I call training you ear. Many people tell me that I can listen to things because my ear is trained (I worked as sound recordist for films and TV), but training you ear is something anyone can do.
Just pay attention and try to separate the different sounds you hear. Anyone with healthy ears can listen to anything, that is not a "golden" thing, as many call it. If I can listen to something, you also can. You just need to focus.
About the meter points, of course you should be careful, particularly when you can short the output to a power pin, or short circuit a power pin to ground. Meter probes should be kept clean, as they do tend to oxidize.
Digital meters, good ones, are now very good, quite cheap and a good investment. Mine is a Mastech, which was cheap and is very precise.
Get yourself some good meter probes with small tweezers. Now you can find some designed for SMD components, which I haven't got yet. But separate cables with points that can grab the pin or wire, particularly the ground, are important.
https://www.sparkfun.com/products/11060
https://www.ebay.com/itm/Universal-...t-Lead-Probe-Wire-Pen-Cable-Hot-/361019706380
https://www.ebay.com/itm/1-Pair-Ban...m=132474589056&_trksid=p2047675.c100008.m2219
Your metering may be right, and the offset be very low, just a few mV. Check any power pin at the same time to see if the probe is fine, and trust what it shows you after several tries.
If the offset is that low, you can safely bypass the output caps. Remember there are caps ahead in the Schiit, which BTW you can bypass too.
But on the Schiit you have to check if there's no input offset, as it's tubes voltage we are talking about. So maybe you should let them be.