I, like you, am intolerant of any edge or harshness. I am also semi-retired and very much enjoying my increased music listening time. Congrats and best wishes.
One thing I would suggest you do is read this review of your speaker. As JA points out, your speaker can be particular of what amp it is paired to. Look the article over in detail including the measurements:
https://www.stereophile.com/content/joseph-audio-perspective-loudspeaker
As I noted, years ago I owned your same Prima Luna integrated (with stock tubes) driving a pair of VSA VR-33's. Both good pieces of gear but that pairing never really did anything for me. No magic it seemed. Never pulled me in and had me grabbing for one CD after another. Similar to your experience, I did not feel the PL had impressive control/power in the bass. The midrange seemed a bit forward in this system. This was my first tube amp and it really did not do for me what I had read about. In fact, it sounded rather solid state to me. Both were eventually sold.
Fast forward. In that same space I now have a Erhard Ray SET (three tubes total!) driving a pair of Omega Super 7 speakers. Recently added a pair of REL t/5x subs. The result---SYNERGY! Now I could appreciate the "tube magic" I was seeking. Sound that was so live, dimensional, dynamic, with "saturated sonic colors". Even though it is not my primary system, I listen to this system more and more.
I would agree that it would be worthwhile to consider an amp that hopefully will better pair with your current speakers. Sounds to me like an integrated that resists any tendency to sound bright or edgy would be best. I am not sure I would recommend tube rolling with your amp. Way too expensive of a game with an amp that has 14 tubes!
Out of the solid state integrated amps I have heard, I might suggest the Marantz KI Ruby. I'm guessing this would have nice synergy with your speakers. Very smooth without sacrificing detail, great soundstage, powerful controlled bass. That rich "woody resonance" your after should be apparent. Heck, with your budget you could even afford the Marantz PM-10. I am sure it is very similarly voiced.
Good luck in your search.