Cooking Cheap Cuts of Beef I've been trying to find a relatively quick way to prepare eye of round "steaks" (really just slices of a roast), so that they are tender and juicy, but not falling apart. The goal is to avoid having to cook an entire roast, which takes a lot of time and results in a lot of leftovers. 

At first, I sautéed them in a pan, and they came out tough and leathery. I then tried to marinate them in a simple mix of olive oil and lemon juice for 30-45 minutes beforehand, and to tenderize them with a hammer. This, too, resulted in a tough, dry piece of meat. My greatest success with this cut has been to braise it in red wine for 60-90 minutes, though it was still unpleasant to eat. 

Has anyone else been experimenting with cooking slices from an eye of round roast? If so, what have been your failures and successes?
The crucial observation is that cooking a smaller cut does reduce the cooking time, but not that much. Cheap cuts contain connective tissue, which consists of collagen. Converting the collagen into gelatine takes time. The conversion from collagen to gelantine begins at 70C (160F), so it important the braising keeps this temperature.
How long the conversion needs depends on the cut of meet but I think your 60-90 minutes are not long enough. I would make it at least 3-4 hours.

Suggestion: Cook the your roast in one piece. Cut it in serving portions and freeze.
Thaw and warm at serving time.

If you want to speed up the braising process consider using a pressure cooker.