Classical Record Collection Needs New Home

I inherited this collection from a friend of the family, and it's been sitting in storage for some time now. It's all classical.
 

All classical. The first shelf is regular 33 1/3 RPM vinyl, while the other three shelves are all shellac 78 RPM records.

This was carefuly curated by the person I got it from. He noted in each record every time it was played, for example, so you could tell the worn ones and the good ones.

It's a collector's dream!

I need to find a home for it, or it's going to get thrown out. I can't keep paying storage on it. I'm trying to move it off these nice racks and into plastic bins which I can stuff in my basement, but that's slow and my basement is filling up.

As it turns out I'm not willing to list each album for sale on eBay and let them sit there until someone buys them. There's too many and the profit margin is too thin with the difficulties of shipping.

Anyone with a truck want to come pick them up? They're in San Jose, CA and they're heavy. If someone wants to come and cherry pick them, or just wants the 33's, that'd be workable.

Otherwise I'm going to be taking carloads of 78's to the dump, which seems a shame. But I'm not set up to play them right now, and nobody seems to want classical 78's.

Any ideas?