It isn’t easy to transplant any large plant. They’ve had a lot of years to settle in, and major root disturbance can kill them relatively easily. And that’s to say nothing of the weight. Once you’re talking a root ball of more than 18” diameter, it plus the plant itself are really heavy. Rhododendron is fairly shallow rooted, though, so you don’t have to deal with a taproot, in any event. It sounds like you’re talking about specimens that are probably 15 feet tall or more? I can’t imagine moving something that size without some pretty heavy equipment, and it probably won’t survive anyway. Can the plants be pruned aggressively over a couple of years to stop the issues with the house?
Here’s a link that I found that talks about transplanting rhododendrons, but I don’t think they’re talking about anything as large as what you’re dealing with.
https://www.finegardening.com/article/how-to-kill-a-rhododendron