Hi Ryan, I see this question has been answered for a while and hope this might help a little bit.  Within the area I work we have been automating Rumba screens for over 20 years.  Initially different methods were used like DDE but over time all the large scale automation settled on HLLAPI.  In my experience HLLAPI is very fast and it is not the bottleneck for the overall process of getting data out of Rumba.  The delays are in how quickly the Rumba screen can refresh's it' data and relate to the whole stack (eg RPG, AS400, DB2, Network etc).  That is why we have always scaled using multiple TN5250 screens running simultaneously.

Maybe you are looking at some sort of file spooling where it could be that the delay could be caused by the last part of getting the data out of Rumba.