I'm using TechReborn-1.10.2-2.1.17.233, RebornCore-1.10.2-2.13.6.142 and Forge-12.18.3.2422.
The game has crashed when using Refined Storage Importer and Ender IO Item Conduits to the side of the Sawmill. The Sawmill does have the entire multi-block structure.
Crash Log when using Refined Storage Importer:
2017-08-15-5.log.gz
Crash Log when using Ender IO Item Conduit:
2017-08-15-6.log.gz
Edit: MC 1.10.2 obviously

Just tested with input from top of the Sawmill with the Ender IO Item Conduit. Still crashed.

Not reproducible in 1.12

I've checked with xnet transferring wood from chest to side of Sawmill.