Daniel,
To synchronize your analog input and counter operations in hardware, you will need to gain access to your NI 6052E through a RTSI cable. The only other option is to access the board from the 50-pin male connector located to the side of your SCXI-1349 cable adapter. Below, I have included a link to a KnowledgeBase with the breakout pin translation for the SCXI-1349:
Breakout Pin Translations for the SCXI-1349 and SCXI-1346In either case, you will want your NI 6601 and NI 6052E to share a start trigger. However, obtaining a RTSI cable is definitely the best solution.
Good luck with your application.
Spencer S.