Here are two sources of means of restoring a deeply discharged Power Cover.
Both involve removing the fabric and the subsequent plastic covering underneath.
This method is only for restoring the charge state. This method works, as I tried this with a hobbyist RC Lithium Ion cell charger that can do Lithium polymer (the Power Cover is configured in a two Li-Po sacks per pack, the whole cover is a two pack state.)
Because this involves directly connecting at the Lithium polymer sacks themselves, this bypasses the sleep conditions that the USB keyboard sends back in telling when the Surface should charge the Power Cover. And because I am using the RC Lithium charger, and can program to the sack/pack profiles, the charger can safely turn off once these cells are conditioned and fully charged.
Should one uses a direct lead charge method of a hobbyist RC battery sack/pack charger, the Li-Po configurations is in two 3.7Ah, 3.7V packs. All four cells total to about 27.38Wh as a result.
This method COMPLETELY replaces the cells with new ones. But one has to manually know who supplies compatible sack sizes of the same voltages (3.7V per sack) before hand in direct ordering. One will need to know how to use soldering AND heatsink clips to prevent burning when removing the old sacks, and to prevent burning when putting in new sacks.
Amp-hour capacity is sack size dependent. One "can" have a longer lasting power cover at the expense of putting in larger sacks in replacement, but one has to deal with the form of the cover afterwards in containment.
This method is applicable if one already has worn cells that no longer has any usable lengthy charge cycles. It is split into two parts.