If I've understood the situation, add a MONTH_YEAR to your original table, then generate an AsOf table like this:
Jan 2004, Jan 2004
Feb 2004, Jan 2004
Feb 2004, Feb 2004
Mar 2004, Jan 2004
Mar 2004, Feb 2004
Mar 2004, Mar 2004
In other words, just link every month to itself and every prior month. Now you use AS_OF_MONTH_YEAR instead of MONTH_YEAR when you want an accumulation, and a simple sum(VALUE) should give the right total, as it will automatically link to that month and all prior months.
Another answer is to generate the missing months of data for every entity and parcel code, and do the sum in the script like you said, but since most accounts do not have movements every month, that feels wasteful to me. It also wouldn't respond to certain user selections the way I'd think you'd want.