Have a Plan B and maybe a Plan C. I do tight connections all the time. Regularly MCT at ATL, AMS, DTW. I wouldn't try this one without a solid Plan B, just as I wouldn't try an MCT at LAX.
If the planets align it'll be a breeze. If you catch one or more of the potential issues, you'll be out of luck.
VanWyck will probably take 30 minutes with normal traffic. Saturday afternoons are not 2 - 3 AM.
If you don't have Clear you'll get slowed at LGA Security, even with Pre. Saturday has lots of families with kids and seniors, I've seen many long lines at Pre at LGA on weekends.
I got hung up at GE last month with the one CBP agent taking your printed form and comparing it to your passport and holding both up to see if the pictures looked like you.
Possible trek fro the far gates (B55 area)
Hooking up with driver.