Thanks for your thoughts. The bookshelves are built-in and pretty solid, but I'll have a close look at them. Last night I "installed" four bags of R19 insulation under the piano and in corners. The bass boom is gone, but the treble is now definitely too light, so I've overdone it a bit. I'll keep on experimenting and I plan to take some measurements over the weekend.
The most obvious problem I can detect at present is that the front of the bass cab vibrates a bit, despite two glued-on braces and two cross-braces (above and below the woofer).
Would it be a good idea to put in some kind of compressible bracing between the back of the woofer and the front of the cab? Or should I just add more glued-on pieces to the inside of the front?