Not sure why you chose 4.40 as I think most of us who have upgraded these old systems would jump through 4.50.8.

However, since you are working with 4.40, I will say that I have had converion issues when an options file is partially set up (the Migration tool seems to create those "NotSetUp" folders, like there will be ARHCI and ARHCI_NotSetUp - or some such thing). You might try looking at AR0HCI, for example, in DFDM to see if it looks set up or partially set up.

You could als try to manually reinitialize AR_31HCI in 3.71, but it might just fail on another file after that:

You could just remove the AR data and/or module in 3.71 and re-migrate. Intersting issue, good luck.

I think you can go from 3.71 to 2017 to 2023.x. 

I have these notes on why 4.5 PU8 is frequently mentioned as a possible intermediate stop: 

• The reasoning behind the decision to require users to be at 4.50 PU8 to convert to 2018 (6.0) is below:
  • All modules except P/R, J/C, W/O, and MRP would have previously been converted to framework levels, and the bulk of the extensive conversions would have been completed.
• The conversion checks the version, not installed modules, and we could not change this requirement based on which modules (P/R, J/C) were or were not installed. 
• 4.50 PU8 contained the ACA (Affordable Care Act) and IRD compliance schema and code, which minimized the conversion to 2018 Payroll

Had to go deep on this one.  AR_31 is a credit card file.  Since each of the companies mentioned is missing the file, try copying the file from a company that converted.  Be sure to change the company code AR_31XXX.soa