Today, aside from spending a lot on washing machine repair for our broken washing machine and waiting for the repair guy to meet his "scheduled" appointment of between noon and 6PM, I figured out that the connection for the clutch sensor switch wasn't connected. That's the one that allows the bike to be started if the bike's in gear already as long as the clutch lever is pulled in. It was just barely sitting in the socket under the handlebar on the clutch side, but was NOT actually connected. A long, thin screwdriver and a couple of pushes took care of that (couldn't get a finger in there, but the screwdriver did the deed fine).
Hey, presto! Bike starts in gear with the clutch lever pulled in just fine, now.