I know what you mean, I have been stuggling with good jazz tones too.
A few nights ago I played with the Fender Bassman standard and that bottom end was getting too much.
The mic choice helps on the cabinet and a couple of EQ instances to balance the tone you want, befor and after the Amp block.
You might just try looping a few chords and fills with the looper in the pre mode and then tweak the Amp pages especially mic choice and resonnace. Also a 60-90ms delay inserted in the block can be used to get that roomy tone.
My advice is to take a few breaks saving what you got before you break and then come back and continue saving to a new tone. This way tyou can then audition your patches once your ears are fresh.
when you get something you like, save it as a patch and move on.
It is a good idea to go for tone matching as you are doing and as you are only on the HD two days it takes a little to come to grips with it.
Really go for your Amp tone first and then a couple of EQs to smooth your response.
I like the 63 Spring Reverb but the ducking one might be the ticket.
Good luck with your jazz tones, not that mine a that good but I am getting some half decent funk tones.