So far as bass goes, I never felt Cary was the last word in bass extension to say the least. They have a very rolled off presentation at the frequency extremes with an emphasis on the midrange with is quite full and present. Now the issue about the sound being tinny is a real dilemma. The Cary should eliminate any tendency in that direction, it is the anthesis of tinny sounding so it seems to be an electrical problem/issue, polarity as suggested above or possibly a mismatch with the impedance/capacitance of the cables in conjunction with the output impedance of the pre-amp, just a thought but a real possibility. You may want to check with the manufacturer of both to find out.
So far as tube swapping, this should not be an issue with tinny sound but tubes can have an impact on perceived bass, quietness, dynamics and frequency extension which is dependent on the electrical characteristics of the tubes. Bass control is pretty much the domain of ss and some OTL amps in my experience. Tube amps with transformers generally do not offer this control and I have not heard any Cary amp that does this well. You are used to the ss amp which is almost certainly better in this area of performance. NOS tubes generally have higher voltages with greater quality control than the ones currently being manufactured. There is a reason people are willing to spend big bucks on tubes beyond the plecebo effect that the uninitiated, inexperienced and non-believers might have you believe. Dwindling supply drives the prices up but the demand is still there, for good reason.
Cable matching with a system is a tweak to be sure but you would be amazed at how properly matched cables can affect the overall performance and enjoyment of an otherwise good system. I have heard cables that have had a greater positive impact than some components so don't discount this because some disagree, listen for yourself before taking anyone's word. Good luck and please report back to us as to the problem.