Cooking Cheap Cuts of Beef
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.