Galen,
Good question. I guess the reason is that JTQUOTA isn't like other quotas, in that it's only used once - when the process is created - to set quota on the job logical name table. Management of the quota is then handled by the logical name subsystem, just like it is for any other shared logical name table.
Although there is a JIB$L_JTQUOTA field in the JIB, it doesn't look like it's written. (If it was, you could figure out the JIB address from the translation of LNM$PROCESS, then calculate the cell address with offset JIB$L_JTQUOTA and access the location directly using F$FAO)
If you're confident that the process was created through the UAF, you could use $GETUAI with item UAI$_JTQUOTA to look at the UAF record (no privilege required to read the record of the username of the requestor).
There is no public API to get at the quota fields in logical name table structures. Looks like the best you can do is parse the output of SHOW LOGICAL/FULL Perhaps it should be an item in $TRNLNM?
A crucible of informative mistakes