I`m not sure how the serial VIs affect the mutithreading of the LabVIEW environment, but setting LabVIEW to run multithreaded and running the two operations independent of each other (in two while loops without data-dependency between them) might do it. You will find the option for multithreading under "options". Bear in mind that a re-start of LabVIEW is necessary before the changes come into effect.
I would time-stamp the reply of the drive with the time of the request, not after receiving the data.
Hope this helps
Shane
Using LV 6.1 and 8.2.1 on W2k (SP4) and WXP (SP2)