You are correct that you will need to re-check your bags after customs and will then be landside. You have a few options:

1. The airside shuttle now goes both ways. You can go upstairs, clear TSA at Terminal E, and take the shuttle from E13 to Terminal A.
2. You can take the Route 11 free airport shuttle bus to Terminal A as JPG3392 said, which runs pretty frequently from the curb on the lower level directly outside customs at Terminal E.
3. You can take the elevator up and walk through the central parking garage to Terminal A. There are moving walkways but it still takes about 10 minutes.

The airport provides an interactive map at maps.massport.com.