I haven't drawn a tag, but went with a buddy who drew a few years ago.
My best advice: It is a once in a lifetime tag. Take as much time off and hunt as much as you can.
The buddy I went with only hunted in his unit for 4 days and then ended up shooting a small bull up by an elk farm North of Minot. To each his own I guess, but that is super frustrating to me when guys like that draw a tag and don't even put any effort in.
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I think we were in E3 as well. We stayed at a place just west of Medora...Buffalo Lodge or something like that. The locals know where the elk are, but are pretty tight lipped. We saw a giant bull the last morning out driving up to a spot to glass. Unfortunately he and a small group of cows went onto a piece of private ground. The private was posted and owned by a guy up in Minot. When I called him to ask if we could hunt he said "No, those are my elk. We get land owner tags and shoot those elk ourselves."