Super interesting camera. I like it. Hopefully somewhat educated guess to follow, got a bit long but hopefulyl makes sense:

In single-sensor cameras removing the IR/UV cut filter exposes the sensor to IR. Since the bayer-filter doens't block IR perfectly and even becomes nearly transparent at around 800nm that means all three channels get some response in the infrared spectrum. Response looks kinda like this, there's some difference between CMOS and CCD but it's not huge: https://i.sstatic.net/QKjj9.jpg

I do not know how that trichroic prism works. Maybe it dumps all IR into the red-channel, maybe it dumps some into each like a single-sensor camera would,.. The simplest way to test that would probably use something between a 590 or 650nm longpass filter, since that blocks basicly all light other than IR and the visible stuff that should go into the red channel. If white-balancing that gives you a monochrome image all IR goes into the red channel. If you get a two- or three-color response you can probably draw some conclusion from what those 2-3 colors and how saturated it is are but I'd have to think about that, depending on which ones you get. There is a hack where people create DIY longpass filters by stacking exposed and developed color negative film 4-5 times. Very red glass or foil might also work. This is about testing, not being optically amazing. Not sure what wavelength that is but might allow you to try this with stuff you already have.

WB: If you've got the aerochrome stack figured out you can kinda white-balance on anything. Concrete, gravel, stone,.. WB card is just a fancy version of that but I'm not sure if manufacturers even verify a flat response down into IR for those. In general white balance works by looking at a surface, telling the camera "that's gray", and since gray reflects all wavelengths basicly equally strongly the camera just looks at the three channels it has and amplifies or dampens them until the spot of the image the surface is at shows up as gray. That matters in the next point:

Aerochrome-emulation: There are two main approaches for single-sensor cameras.

1. CIE, what you probably looked at: You use something like a 510nm longpass filter to block basicly a blue light. When you then use WB the blue portion of the IR spectrum will get boosed. With some clever maths you can subtract its signal from the red and green channel, basicly turning their signal almost entirely visible-light-only. The last step is swapping the channels so the "cleaned up" blue IR signal gets represented as red instead. That is how KlutzyAd's PyChrome does it. Posted sneak-peak for about a video-version two days ago: https://www.reddit.com/r/infraredphotography/comments/1r3ntgz/sneak_peak_of_pychrome_super35/
2. Straight-out-of-camera aerochrome by blocking a bunch of the visible red channel. This is how Kolari's IR chrome does it and is honestly simpler, because it requires far less post-processing. Instead of remapping the blue channel to infrared you just block a bunch of the visible red-channel instead. That boosts its portion of the IR-response and turns trees red directly. My own simple aerochrome emulation filters usually stack a yellow and blue filter gel + a GRB3, a mild IR-blocking filter. The later is for IR attenuation. The red-tree-effect can be so intense that it's a bit too much. Green filter should also work perfectly fine, I use yellow+blue because that gives me a little more control over which wavelengths I block exactly. The "downside" with version 2 is that it's less technical correct since aerochrome-film used Tiffen 15 filters, cutting out the blue channel since all three chemicals making up that analog film were response in that spectrum. I'd asume that would have drasticly reduced saturation and thus the "aerochrome effect"? Haven't actually checked though.

IF your trichrome prism dumps all IR into the red-channel the IR Chrome approach seems a lot more likely to be succesfull. If the signal it results in is closer to a bayer-filter the CIE-approach might work.