I agree with the comment to get rid if the EH tubes. I have two Jolida amps and have done a lot of rolling. My favorite combination is the new Tung-Sol reissue ECC803S to replace the 12AX7, the GE 12AT7 where applicable (yes, the lowly GE) and Ei 6CA7 fat bottles for the power tubes.
The Tung-Sols are the only current 12AX7 I like and the only one that doesn't lose out to the 5751. I like it a lot. The GE 12AT7 is very inexpensive and is a little on the warm side, which balances the Tung-Sol nicely. The Ei fat bottles can be had from Kevin Deal at Upscale and are far less strident than many of the current production types.
In order of priority, in my opinion, would be to replace the pre tubes, then the power tubes, and the 12AT7s last.
Having said all that, I do not find Jolida amps to be particularly problematic when it comes to stridency. The Mullards in the pre section would certainly warm things up...maybe too much. I find them to be a bit too much toward the Yin, but they do offer a very nice and warm dimensionality to the mix. I certainly see why some like them.