Switching over from old SPG to new Marriott account went without problems in the app.

However, same as with OP, my lifetime status is also showing incorrectly right now (Lifetime silver instead of platinum premier elite status - I should have 10 years Platin and 791 nights). I contacted SPG I’m sure that’s something that will be fixed soon.
Luckily in my case, I had lifetime platinum with SPG and app shows 791 nights now. So I don’t think there will be any need for me to prove anything.