Meat – what kind of meat is used at carving stations

I'm going to assume that "country style ribs" are the ones where you cut them apart first before cooking ... I'd wager a guess that everything is near bone, and a thermometer might have problems with this particular dish. If nothing else, as you can't insert it deeply enough into the thing you're taking a measurement of, there might be enough conduction along the probe for the oven temperature to throw off the reading.

Could you tell us how far the probe was in the meat? I'd assume anything less than about 1/3 the probe might be problematic, with 1/2 or more being better.

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All of that being said, are you sure it's an issue with the placement of the probe, and not a problem with the probe itself?

I've had a number of them go out over the years. I've actually given up on them, and gone back to an instant read thermometer, as I'm up to 4 of the bases (can still use 'em as a timer), and no working probes. (if anyone knows any brands that sell the replacement probes individually, or even better in multi-packs, I'd be willing to go back to using them)

To calibrate -- mix some ice water, and put the probe in there. It should read 32F or 0C. (if it even goes that low, not all do). Boil water, and read the temperature of it, and it should read near 100C or 212F (possibly lower, if you're above sea level). Compare it to another room thermometer after it's been sitting for a bit ... they should read the same.

Don't try to put it into the oven directly ... you could melt the probe ... that's how I lost the first one, so you can't try to compare it to your oven thermometer.

There is no single cut of meat that is universally used in Philadelphia. Top round is common, and it may actually be the most traditional given the sandwich's Italian origins (top round is what is used in braciole and Italian beef sandwiches). It is becoming more and more common to use rib-eye, though, which is what is used in some of the most popular Philadelphian establishments (e.g., John's Roast Pork and Tony Luke's), which makes sense given its higher fat content.

As lazoDev mentioned, you should be able to get your butcher to slice the meat into thin (~1mm) pieces. If that is not possible, though, you can put an entire rib-eye roast into the freezer for a half hour or so. This will harden the meat without actually freezing it solid, and will make thinly slicing by hand much easier.