Thanks for posting the
pic of the OB system, Smirkr. If I could offer a suggestion it would be to fit a 5"-6" class midwoofer where the Beston ribbon is located now, and then just mount the ribbon onto the top edge of the baffle itself, e.g. "sitting on top", right above the midwoofer.
This placement of the new midwoofer will benefit from being close to the edges instead of central on the baffle, which is important in the band extending up to 1k-2k and slightly above. Cross the 8" to the new midwoofer around 750-800Hz and take it up to 2-3kHz before crossing over to the ribbon. This should help the system sound better in the critical band around 1kHz.
Some possibilities for the new midwoofer, that I have personally measured and used in OB systems, are:
Audax HM130C0
SB Acoustics SB17MFC35-4
Peerless NE180W-04
The best one of the above three for your application would be the Audax (it's a 5.25" driver). The least expensive is probably the SB Acoustics.