Bravizzel, I feel your pain - we are going through this exact situation. I don't know if it will help but we've gone with a risky "all in" strategy based on...
1. School was number one. My absolute priority is making sure my kids start their school on day 1 with the rest of the kids. This in effect set our target move date to mid-August at the latest.
2. Next was a house (flat!) to live in. I am lucky in that my job has sorted out a place to live, even without that though, I don't get a sense that planning on a month in a serviced apartment while you find a permanent home is particularly risky. There are others here that could tell you about this more accurately than I though.
3. We are renting out our house while we are away. To hit the "sweet spot" in the rental market here we have to be out by the 31st of July.
4. Working backwards we should have applied for visas in May. My office didn't even given final approval on the move until mid-June so that was a non starter.
We were left with a choice of play it safe but miss some key dates, or take a punt on it all working out and hope for the best. We decided on the latter, have sold one car, rehomed pets, signed a lease to rent our house out and are moving out in 2 weeks. Still waiting for the visa though, so not sure if we're moving into the hotel down the road or beginning our adventure. Technically, moving 4 of us with as much luggage as we can carry into a hotel will be an adventure of sorts anyway ;-)
Your mileage may vary - it all comes down to priorities and risk. We could end up with all sorts of egg on our faces and beyond if the visas fail for some reason. Fortunately I work for a company where this is fairly common so we figured we were reasonably safe on that score. And anyway - once you've wired HKD $250k odd to the school you're kind of committed anyway!
Good luck!