Does Yogacara and its Alayavijnana fail compared to a Permanent Self?
Shankara is Advaita Vedanta, a branch of Hindu philosophy inspired by Buddhism, so why are we talking about him? I guess you were reading his critics of Buddhism and this is what you ask? 

Your confusion about "infinite regress" comes from your materialistic assumption that separate objects exist in and of themselves, without observers. But in reality, separation into objects is a feature of the observing mind. 

The observing mind does not arise all at once but emerges gradually from impressions of interactions. These impressions and interactions are automatic and undifferentiated, they have to accumulate until the patterns in them become obvious enough so that individual objects can be delineated. The mind is nothing other than the sum total of these accumulated impressions giving rise to an ability to recognize.

It's not that nothing exists prior to the delineation, but whatever does exist is not delineated, so before delineation there are no separate objects to talk about. The boundaries between objects are arbitrary and are drawn by the observing mind. Different beings delineate different objects thereby creating their specific subjective realms. The desires beings have are for those subjectively delineated objects. 

What you call substratum is nothing other than the cyclicaly dying and reemerging medium of living beings. They are the carriers or the bearers of the samsaric mind. This mind is partially taught to and partially reinvented by every newly born baby. No permanent self is necessary because beings take turns carrying the torch of the samsaric mind and passing it on down the line.

Alayavijnana is the sum total of information carrying forward by the diversity of media that the samsaric mind can draw upon as it recreates itself in the new generations of sentient beings.