collection shipped overseas

Sorry I forgot to say, line the inside bottom with bubble wrap.

'I would surround the LPs with solid foam.'

Elizabeth, I'm assuming that your referring to standard foam or standard packaging foam with which I have to respectfully disagree. Foam Core is light weight, rigid and with exception to the corners, relatively damage proof in packaging situations. A sheet of foam core can be bought cheaply at art supply stores and cut down into squares with a straight edge and X-acto knife or razor knife. Foam core is uniform in thickness, typically 1/16 inch.
I would also suggest using a roll of cloth tape to bind the two pieces of foam core (1 piece of tape on each end) at the bottom while leaving the top open for easy inspection by customs. I'd send them in three boxes while wrapping the entire contents in a solid sheet of plastic with the opening at the top.

All of these suggestions in heavy cardboard boxes will work like a charm but I'd still ask UPS if it would be best to double box them.

Pack each record in a separate box that can be found on the Uline site. Best way of shipping. In any event, your venture will be expensive, maybe as much as $5.00 each.

The jackets won't give you any protection. I'd put each record between sheets of foam core.