A couple (actually five) thoughts:
1. Having the insurance company pay to have the mold damaged records cleaned will not return them to their full value as CZ noted above. If the insurance company would treat them as a total loss and you could be compensated accordingly, that would be the best option (unless you have rare, irreplaceable pressings).
2. I wouldn't assume that conventional record cleaning methods, including ultrasonic, will kill that stuff. (Aside from not wanting to pollute an ultrasonic machine with a living organism). I haven't really researched cleaning moldly records in depth, but my impression is that you need something pretty aggressive to kill that stuff. There are various mold remediation chemicals, some of which may be suitable for vinyl- I think one fellow on the Net was talking about Sporicidin, but I have no hands-on experience with that, and as I think the Record Genie noted, some mold may have 'etched' or damaged the record so even if you kill the active growth, the damage is done. You also have the issue of not using something so volatile that the cleaning does damage.
3. If you are going the cleaning route, I would go with a professional, like the Genie (who I have not used, and have no hidden agenda to promote).
4. As others have noted, get the records out of their damp sleeves and jackets, pronto. That stuff is alive! And keep all of it segregated from other things; I would imagine mold on vinyl could migrate to other things within your household. Not to be alarmist, but you have to treat this like the biohazard that it is; I would think touching the records or sleeves, and touching other stuff in your house could cause contamination, but maybe i'm being alarmist.
5. Bummer. Hope you get this sorted. It's an issue I've thought about researching more fully, but I haven't had the need (thank goodness) or the time. I didn't see much on the web in the vein of archivist recommendations regarding vinyl records, there are some pieces about mold on books and documents, but that's a whole other thing. (And they are wearing gloves too).Nor was there anything I saw in a quick glance on the Library of Congress guidelines on archival matters re mold remediation for records. (I didn't look real closely but I don't remember seeing anything).
Let us know what happens, and I'd be interested to hear from the Genie, if he does do this kind of remediation, exactly what he does (unless he considers it proprietary).