End of story:
After experimenting with recapping the crossover of the 10pi, I finished with the following capacitors:
Jantzen Superior Z-CAP for the 10uF
JB capacitors (JFX 220) 2X 20uF (=40uF)
Mundorf MCap MKP Classic for the 100uF
Bennic NPE 2X1000uF + 1x500uF (=2500uF)
I did not use bypass, but because there was no equivalent to the 2,500 uF I ended up cascading them as above.
As you can see, part of these are high-end expensive caps.
After burning inn period, I found the result better than the original speaker. Highs became more present and sweet, but there was also a considerable improvement to mids and bass. I love the result.
Thanks for all those who helped and guided me in this jurney.
Menachem