Yeah, your suggestion is the only thing I could think that would even work, but honestly, it’s probably more trouble than it is worth.
An alternative which doesn’t quite meet the requirements, but will be much lower effort would be to format the drive(s) as exFat, which both Windows and Linux can read without issue. Then put them up as a network share in both OSes.
If you are wanting RAID 1 with those two drives…this won’t work unless you are either using hardware raid (maybe you can set it in your bios?) or if you can find a software raid that both windows and linux use. For RAID, maybe just pick one OS and that will be the one that has the share.
I would also recommend against the SSD caching idea with all this other stuff in the mix, wait till you have a dedicated NAS PC. You are going to pull your hair out otherwise.
OP, do you have an old computer, even an old laptop? A NAS doesn’t require much computing power. You can plug your drives in via a SATA to USB adapter. Then you will have a dedicated NAS box and all these problems get 500x easier.
There are companies that do freight forwarding. Much less dodgy than random person on the internet. Would be worth checking out.