In the mean time, this was a perfect opportunity to find out whether my loose-match-and-refine strategy only worked when I was doing my own relatives (with all the odd tidbits of half known information to help me sort through the possibilities) or if it could be made for an unfamiliar family tree.
The answer, as anyone could have predicted, was a little of both.
Currently, I've been working on the ancestry of the woman who married into the shared last name. She's a Delp. We're really clear that she's a Delp; that's not in doubt. I thought I had identified her extended family (siblings, parents, people they married, the kids they had, etc.), but one of her sisters married a Lottman whose mother was a Delp. That actually was great: first cousin marriages are usually a sign you've got solid clan-behavior going on and it's virtually impossible to screw up unless you're really not paying attention.
The problem was that Lottman-Delp marriage. He was Illinois, through and through. She was Iowa through and through. How'd that happen?
I spent a bunch of time tracing everyone through various census records to be sure this really was a cross-state clan, and not a matter of name-punning. When I had Lottman as a young man, working as a servant, three pages away in the census from Delp as a slightly younger woman, in her father's household, it became impossible to imagine that name-punning could explain what was going on.
If only I could trace them back to Ohio, where they supposedly came from, at least according to some census records. I did find a copy of _Delps Galore_ online; I'm awaiting its arrival, in hopes it will shed some light.
My husband is currently very excited that some New Hampshire indexes are now available through ancestry.com, thus enabling him to make some progress in advance of a hypothetical future trip to a genealogical library a little ways north (either the one in Concord, NH or the French-Canadian one in Merrimack, NH).