It sounds like things get significantly less complicated on the return if we fly carry on only, am I right? If what I'm understanding is correct, we should be able to check bags in DSM through to LHR, but on the return, while we may be able to check bags LHR to DSM, we'd still have to collect them in MSP?
I believe our tightest flight would be 7 hours prior to boarding in LHR on the return, so I'm hopeful we're good there...but while I'm generally a pretty big risk-taker, I also don't want to risk missing the long-haul either way. I'd prefer to fly DSM to MSP (I'm bringing my parents on this trip and car rides are, shall we say, challenging), it sounds like 84fiero is right that may be my safest option!