Look, the people are nice. They're even generous with the meat (not cheap, but a fair value). But, this place is not, as billed, a Jewish deli, Chicago-style or otherwise. A reuben, for example, is NOT made with cold corned beef on plain (not even toasted) rye bread, and adding sauerkraut and dressing (both also cold, of course) doesn't make it one. The reuben a a GRILLED sandwich, i.e., hot (or at least warm). If you've never been to a real Jewish deli, and the owners obviously haven't, the least they could do is look in a cookbook.
BTW, I'm not myself Jewish, but I hate to see any ethnic cuisine so poorly executed. It's bad enough how hard it is to get a good reuben in this town. A place styling itself as a Jewish deli should be the one safe haven in the storm.