Your approach of just including the field term on the left side of each bond, then also including the right-side field term on the last bond looks very reasonable to me.
If you aren’t getting the results you expect, I’d just suggest checking over all the details very carefull and trying limits like N=2 sites. It’s really good that you are comparing to ED.
When you say the results don’t match ED, are they very different or just a little bit different?