So digging into all your examples, BSPs, and the ASRC library itself I cannot seem to see how converting from 44.1k will work.
The way your examples show conversion, buffering, DMA, etc. is all setup for sample rates divisible within the 1ms USB period (ie. 48k, 32k, 16k), but I do not see anything related to non 1ms divisible sample rates (44.1k).
Do you have any examples and documentation showing the use of 44.1k systems (whether using the ASRC or just generic 44.1k based systems)?
Right I cannot see how, the way your examples are setup, they can handle 44.1k.