We have a JFW RF Transceiver which acts as a sort of hub, and allows us to connect each radio via coaxial cable.
I've never heard of "JFW RF Transceivers", but your description sounds like a channel simulator / emulator, or maybe just an RF switch matrix, not at all like a transceiver. (a "transceiver" is a device that is used for communication, which combines a transmitter and a receiver. Your mobile phone is a transceiver, and so is your laptop's wifi card. Your kitchen FM radio is a receiver, and the device that was used to simulate the channel from basestations to the multiple antennas of your mobile phone during development is a channel simulator.)
The new radios have MIMO, and I am unsure how to connect them, or if MIMO will even work with the radios connected via coax cables instead of transmitting over antennas.
You need to realize that MIMO stands for "multiple input, multiple output": by its very definition, you only get a MIMO channel if the transmissions of multiple antennas add up "on the air" and that mixture is received by multiple antennas.
My initial thought is to connect each antenna port from each radio to the transceiver. Our transceiver has 8 channels, and each radio uses a 2x2 MIMO configuration, so this would require 4 channels for each radio. This would limit us to connecting only 2 radios at a time.
It would make sense to only connect 1 TX and 1 RX port of each transceiver.
Second question: Can I combine TX / RX MIMO antenna channels on a single channel on the transceiver? How would I do this? Just use a BNC splitter in reverse?
These are three "second" questions :)
but: yes, combining the transmissions on the medium (usually: air, here: cables) is what a MIMO channel does. You'd do well learning the basics of MIMO, they seem to be relevant to understanding what you're doing at all!

MIMO Channel visualization. This is for the one transmitter, one receiver case. If you have two transmitters and one receiver, you get two groups of transmit antennas, whose signals also experience their own channel coefficients \$h_i\$, and get added up at the receive antennas. The fact that these \$h_i\$ are different and at least partially linearly independent forms the basis of MIMO.
You will only get a performance that is comparable to the over-the-air case if the receiver channels receive a "mixture" of the transmit channels that is different for each receiver channel. In other words: ideally, the channel matrix needs to have full rank.
So, BNC splitters alone won't do. You will need to split each of the \$N_T\$ transmit channel to \$N_R\$, the number of receive channels you have, then apply a varying (e.g. random) phase and attenuation (e.g. through cables of different length, and varying attenuators) to each of these \$N_T\cdot N_R\$, then sum groups of \$N_T\$ signals to get \$N_R\$ receive channels.
Typically, this isn't even a good MIMO channel emulation for practical systems, because very commonly, MIMO is applied to wideband channels, where you get frequency selectivity for different paths, meaning that the channels are not only diverse for the \$N_T\cdot N_R\$ different paths from the transmit to the receive antennas, each of these paths also differs over frequency, so that you're less likely to have a receiver path that's "universally bad".
Specifically, to use fewer channels so we can connect more than 2x radios?
You're throwing away the MIMO capabilities of these radios if you don't offer them a MIMO channel, and that might (will) degrade their capabilities. How much reduction you can tolerate is up to you – but you don't buy or worse develop new MIMO-capable radios to simulate a modern mobile ad-hoc network (MANET) if you then omit MIMO, if you ask me – that would basically mean you spent money to travel back in time by 20 years technologically.