I have two 128GB SU800s, which died at approximately the same time. One drive isn't detected by the BIOS; the other is detected in Windows, but any data access to it results in it "hanging" (hard drive activity LED stays lit), and then it drops out and disconnects - Windows stops seeing it.

Any ideas on what I might be able to look into at home? Or is this a case of sending it into data recovery pros?

The drives were part of a Storage Spaces pool, and since they're part of a 2-disk mirrored tiered space, my data on the affected volumes are toast

yes

Yeah, you likely need a pro and due to the complexity of failed SSDs, compounded with Storage Spaces, it isn't going to be super cheap, but shouldn't be insanely expensive...depending on the extent of the damage to the SSDs. I can't speak for other lab pricing, but my lab currently does single SSD recoveries at a $750 CAD flat rate (~ $525 USD). If we have to deal with both as a RAID, it is double that.

Although I'd be happy to help, the reason for my pricing is just to help you have a starting point for reference.

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Luke
Recovery Force Data Recovery