I have one of these particular adaptor boards, so I am familiar with how much of a problem they are to fit into the standard dip sockets. The particular problem you are facing with the over-height socketed chip is new to me.
Might I suggest the following?
Unsolder the current pin-strips and sockets from the adaptor board. Solder in new strips with longer legs, and then resolder the sockets back on the adaptor board.
It might take a while to do, but at least it would leave your motherboard intact. Alternatively, exxosuk has an adaptor board here that will definitely fit your board: https://www.exxoshost.co.uk/atari/last/storenew/
I am, however, making the assumption you are okay with a soldering iron, how far are you prepared to go to fix things up?