Hi, You mention several factors(low light, foot trafic and poor soil) that make it hard for shade tolerant grasses to flourish. Shade grasses do not tolerant foot traffic very well, and recover poorly. White Clover has a strong root system once established and does well enough in nutrrient poor soils. The mix should contain both clover and shade tolerant grasses. Fine fescues would be a good choice. Foot traffic could indicate a soil that is compacted and that should be dealt with core aeration. Aeration can be done every year in problem spots.
If at some point you no longer need the clover, you can use a herbicide. the down side could be the possibility of the clover getting into the lawn next door.
Hope this helps.