We did it last time (on a much shorter trip -- 3 nights onsite at Universal, 3 nights at the Beach Club, then 2 nights at the Polynesian). Our reasons were much the same as the OP's: for the Disney leg, we'd always dreamed of staying at the Polynesian, but it wasn't going to fit the budget for the whole stay, so we split it. (We were staying in DVC studios on rented points, so the price differences were probably different from the norm: for our dates, it was $250/night at BC and $411/night at the Polynesian).
We had no issues at all with the move and didn't find it very inconvenient, BUT -- and this is a big BUT -- we are light packers, we don't tend to spread things all over our hotel room, and we packed specifically to accommodate the move. By that, I mean we each had a single 21" carryon bag with 5 days' worth of clothes, PJs and swimwear packed in packing cubes color-coded for each person. I did laundry on our second day at the Beach Club so we could "reset" our wardrobe for the second half of the trip. Other than our "cubed" clothes, we had only a couple of dopp kits for toiletries/makeup, a foldable little bin of breakfast items, and a packing cube of sundries (e.g., phone chargers, disposable ponchos, clothespins, laundry bag), all of which could just be unzipped and tossed in a dresser drawer or under the vanity when we unpacked.
Packing in this modular fashion meant that packing up each hotel room, and unpacking it again at our destination, took about 5 minutes each time. On our "hotel switching" day at WDW, we simply dropped our carryons with Beach Club Bell Services on our way out to rope drop the MK (with instructions to transfer them to the Polynesian). Although we usually take a mid-day nap/pool break, we structured our "moving day" differently to minimize the pain of temporary homelessness: we stayed at MK until after the 4pm DVC check-in time (lingering to see the 3pm parade, which we usually miss). Then we took the monorail to the Poly to check in, head to the room (our bags arrived within 10 minutes of our calling for them), relax by the pool and enjoy a dinner reservation at 'Ohana. Because we also structured our touring to take advantage of our transportation options (going to Epcot and HS via boat/walking path while at Beach Club, and MK via the monorail while at the Polynesian), we felt like we really got the best of all possible worlds.
I wouldn't recommend a split stay to everybody, however. If yours is a party that just really likes to "use the space" and spread out in your hotel room, or if packing and unpacking are a lengthy and/or stressful process for you, then doubling the amount of times you have to do it on vacation might be more hassle than it's worth. Ditto if you have small children who need a nap every afternoon and would be overtired for the day if you weren't able to get into your hotel room on "moving day" until after check-in time. However, if you see the hotels as attractions unto themselves, are torn as to which ones you want to try, and intend to take advantage of different' hotels' proximity to different parks (and/or their onsite dining options), a well-executed split stay can add fun and excitement to your trip.
