There are a number of different formats and I don't think CameraLink has that broad interoperability, but an option could be a CameraLink to Gigabit Ethernet converter module. A lot of high speed/high data cameras will use CameraLink but have modes that aren't as bandwidth hungry (like low resolution images), or are just old enough to not need excessive bandwidth, but while there is some free software for this kind of thing, hardware and software compatibility can sometimes be specific to particular hardware.
There are also PCI and PXI/PXIe cards with CameraLink connections and you can probably find some PCIe cameralink cards <$500 on ebay without too much issue. Yeah, still expensive, and a gamble unless you have access to the manuals or software, or even have experience with the platform and workflow... but as you said, if the manufacturer wants you to inquire for a price, the price of the supporting accessories may not actually be all that steep.
I have seen some other SWIR band cameras with regular old USB 3 or gigabit ethernet, and depending on your usage, that may do the job for your application - these ones only seem to be rated to 2.9um, so they've only got their toes in the MWIR band. I can now confirm from testing that somewhere around 150-200C you can see heat emission in SWIR (<2um), so if you're looking for high temperature analysis, that could be an option instead.