A large XS of aspirin should not cause problem with extraction.

Amides will be inert to hydrolysis, even with a strong base.

If the acidified post reaction mixture was initially extracted with Xylene, there will be very little of the amide remaining to be extracted into the Bestine.

The amide will be poorly soluble in Bestine in any event.

Lysurgeons write up doesn't indicate how many bestine extarctions were performed, nor the quantity or temperature of extraction solvent used, so it is difficult to say why the yield was low, whether due to poor feedstock, high NMT content, or poor lab technique.