"All rooms have their own character, but they are not all bad. I think room treatment should be used when needed, but it isn't a cure all and room treatment is easily over done. "
I like that advice!
"I wish I could TRY some different components but I dont have local dealers. "
More and more companies that market via the web offer low or no risk/cost in home trial periods, or satisfaction guarantees. That is the best way to try different things in YOUR room/system.
Buying used and not overpaying off ebay or Audiogon is another way to try things without taking a financial hit. If you don't like what you try, you can sell it with little or no risk/cost incurred.
" I was really impressed with the Harbeth speakers and I had never even heard of Harbeth. "
I'm assuming the Harbeth's have a different sound that you like than your speakers. That might mean you should consider trying them. Or it could mean that the the harbeths you heard were just set up better to shine in some way than your setup. Or a combo of both. Hard to say for sure.
"How can one isolate which component is the reason for the good sound."
Its usually not one component, but how well things work together.
Room/speaker/amp synergy/integration is the biggest factor in general I would assert.
Once you have that down, then you can tweak sources, wires, power, etc to fine tune further.
You have a nice amp. You have nice speakers. You have a room with certain constraints that you have to deal with (everyone does to some extent).
First, make sure you experiment with speaker placement as much as you can to see what is possible with what you have.
Then, if needed, I would do an in home trial of a good high power high current SS Class D amp to compare with your Pathos. That will help you determine what your speakers are capable of doing. Then you can decide whether to change speakers or not, and then work to make sure the amp you go with can take the speakers you like to the max.
As you experiment with different pieces, be sure to continuously work to optimize speaker location in that this can change as things upstream change.
Once the room/speaker/amp combo is locked in, then tweak away as needed, but I really believe there is no reason to consider replacing the Cambridge for a long time if ever. It is a fine sounding unit that should work well in most any rig.