Gatorskins are a beast to put on the rim for the first time. I have never had such a struggle. However, they will fit and once on they stretch enough that they are much easier to reinstall. The 23-25-28 sizing is teh diameter of the tire itself. 700c is the diameter of the rim. If you bought 700c tires, they will fit. Gatorskins are expensive (around $50 per tire) but they are great for avoiding punctures and they last a long time. The flat resistance is worth the extra cost IMO. If you paid much more than that, you should find a new shop.

You can ask the shop to install them and they will probably do so for a minimal charge.

Contls are great tires and you need not be so quick to give up on them.