Chris, no I did not mean to suggest going up (or down) in tire size. I just used a G load designation as an example. (Actually I missed seeing the E in your post.)
All I am trying to say is to check the actual load rating in lbs for another brand with E rating. Not all tires are created equal. It might be prudent to stay with the size provided with the coach for clearance reasons, rim size, etc.
2015 Jayco Seneca 36 FK
2016 Jeep Wrangler Unlimited tow
2010 Tiffin RED 36 QSA - gone
2011 Monaco Monarch class A - gone