First of all, I used a Cary SLP-98P for a couple of years but I got tired of the thick, sluggish sound. I now use a 6SN7 Aikido preamp of my own build, very similar to what Don Sachs was providing before he retired from that business and moved to Spatial Labs. That in turn was based on the Tubes4HiFi SP14 octal Aikido preamp. The Aikido circuit is much "faster" and more transparent than the Cary, plenty of rhythm and pace.
Secondly, I would NOT mess with solid state replacements or different types of tube rectifiers at the risk of voiding your Cary’s warrenty or worse, damaging it. IMHO the Cary sound is determined by the way they configure the 6SN7, and also the type of output caps they use. A lot of folks like that sound but like you, I found it unsatisfying, especially once I heard the Aikido-style preamp.
You COULD try a genuine Mullard GZ34. They tend to be "faster" and a bit more lively on top than most others. A current-manufacture Chinese or Russian 5AR4 will, IMO, NOT get you what you are looking for.
If you want to keep the naturalness and linearity of the 6SN7, I’d suggest a used Don Sachs SP14, or the Linear Tube Audio MicroZOTL or the new Velo, if that’s more within your budget. Also look at the Icon Audio Pure Valve. Another option might be the Black Ice F360, which also uses the 6SN7. That’s my .02. ;-)
ETA: I forgot to mention that the Tubes4HiFi SP14 is still available, and at a very good price. It’s not as tricked out as the Don Sachs version, but it’s a VERY good preamp for the money, one of the great bargains in high-end audio IMO.