I tried it and liked it very much. I'm not prudish about pie. It is what it is.
Just cook at lower temps for longer because of its thickness. The center tends to be cooler than the rest of the pizza.
From what I understand, the owner of Reggio's used to work at Home Run Inn and then left to start his own business. There's a similarity, but Reggio's is cheaper.
If you can get a fresh pie, do it! They're great, but in bad neighborhoods. Go to 87th and Dan Ryan during lunch....it's safe then.