I see from later updates that you did contact Disney - an offer to switch to OKW doesn't seem worth it. I think the suggestion to do most of your MK related business on the BLT days, and do the other parks while at the cabins, is your best bet.
If you DID need to get to MK, or over to Contemporary, where you would have traditionally used the boat, while at Wilderness - the option I'd probably take would be to take the very short internal bus over to the campground, then walk over to their boat. I'm like you - I will avoid busses as much as humanly possible. I never drive to parks, but I seek out any alternative transportation available, with a strong preference for boats, walking, and monorails/skyliner as a backup. If I was at Copper Creek and wanted to get to Steakhouse 71 for a dinner res while the boat dock was closed, I'd much rather deal with a less-than-5-minute bus ride to Fort Wilderness, a short walk through Settlement, and hop the relaxing boat from the campground over to Contemporary and back. Ditto for getting to MK. Sure, the bus ride from Wilderness Lodge is reasonably short to MK, but the boat ride gives me a little dose of zen and relaxation to my day, so I'd do anything in my power to include it, even taking another short bus ride.