I've always played mono records with stereo cartridges. I understand there is less noise with a mono cartridge, which could be useful. However, for me, I put the money into a better stereo cartridge and tonearm.
Rather than split the cost, why not adjust the percentage on the number of mono records you have versus the number of stereo. If you have 30% mono why not spend $7000 on a stereo cartridge and $3000 on a mono? That will help you budget you stereo dollar but how the cartridge sounds is probably more important than just a dollar figure.
Note that all new recordings will most likely be stereo, too. Also note that many mono recordings are not RIAA compensated, so spending a lot of money for a mono cartridge could be somewhat of a waste.