OMG You get my vote for my favorite car on this forum!!! I would die for that car, it's my favorite design Cadillac has ever made. I just don't know about the HT4100 engine but w/e. With that mileage I'd deal with it.
Definitely look for Michelin Symmetry's if you can find them. Check online, call locally whatever.
If you can't find them, go with Falkens, Bridgestone even Hankook are great, they sell Hankook at Walmart now and they have the High Mileage Plus II in pretty much every size. Look into it type it into google. They're really a great tire the H725. I'm going to put Hankook's on my DeVille when I get the money.
Also if you can find Uniroyal TigerPaw AWP II WhiteWall. Tirerack.com has some in stock check them out. Uniroyal makes a great Michelin alternative, they're made by Michelin, I heard great things about them for the price.
I love your Brougham! If you ever want to sell it to someone who will take care of it and treat it right and wax it every month like I would then I'm you're man!
Also please post some more pictures, if you have anymore questions about tires just let me know I'll help you out.