Thank you for taking time to try to help us! Since I posted my update, we also received copies of the transcript of the Arenshorst church book (St.Johannes) with all entries for the Schroeder surname. I spent several hours on the aidaonline site yesterday and the items you've noted are definitely two that I had written down to pursue further.I also searched using Bohmte, Ostercappeln, and Stirpe which are all in close proximity. I've seen the Venne book in the past but at a time when we didn't have as much info so will take another look!
Are you a member of the German SIG with STLGS? Would love to compare more ideas with you. I'm sending you a PM with my email/phone. Thanks again!