Do you plan to eat breakfast at the hotel? If not, the Hyatt Place's free breakfast is not a factor. With an 8 a.m. opening, our family would be out the door at 7 a.m. to make it over to the park, get through bag check, and line up at the Esplanade for rope drop.
Disneyland (and DCA) typically starts scanning guests through the turnstiles around 7:45-7:50 a.m. and holds guests at the Hub for rope drop. Especially if you're hoping to join a boarding group for RotR, you need to be scanned in before official park opening. I also cannot stress how much you can get done between park opening and 11 a.m. Those first 3 hours or so in the parks, before the masses descend upon DLR will see shorter lines, wait times, and be strategic about pulling FastPasses (or MaxPass if you decide to splurge).
Another thing to consider is Disneyland Park has its EMH/Magic Mornings on Thursdays and Saturdays. Disney California Adventure has its EMH on Fridays. So while the official opening time for the parks is 8 a.m., Disneyland will already have been open an hour before that, since 7 a.m., on Thursday and Saturday, and DCA will have been open an hour earlier on Friday. This means if you're not an EMH guest, even if you're lined up for an 8 a.m. opening at a park at has EMH/MM, you'll enter a somewhat crowded park and be at a disadvantage for FastPasses and lines. (I believe the early entrants still have to wait for official park opening at 8 a.m. in order to join a boarding group.) You may want to open up the park opposite of EMH/MM, i.e., DCA on Thursday and Saturday, and Disneyland on Friday.
What our family typically does for "breakfast," when we're staying at one of the offsite hotels along Harbor, is if there's enough time once we get in line, we'll place a mobile order at Starbucks next to the World of
Disney store in Downtown Disney (note there are two Starbucks locations in DTD, so you'll probably want to order from the one further east, closer to the Esplanade), and I'll run and grab some coffee, drinks, and pastries to bring back to the line. We'll juice up and eat in line or at the Hub waiting for rope drop, which usually tides us over well enough until lunch when the crowds start getting heavy.
If you do plan to move hotels (and we've done this), what I'd do is wake up a little early the morning of the move, pack up everything you can (or do this the night before), then come back to the hotel around 10-11 a.m. (when the parks start getting crowded) to finish any packing that's left, get your bags, check out, and take an Uber down Harbor to the Fairfield, check in. (Or just send DH?) Then you can grab a bite to eat offsite (there's a Pizza Hut kiosk at the Fairfield, a McDonald's and Panera Bread nearby) or head back to DLR and grab lunch in the parks, hotels, or DTD.
The Fairfield is a LOT closer to DLR than Hyatt Place -- about a 5 minute walk across the street. Normally, I'd recommend against utilizing the Toy Story Shuttles, because I don't think they save very much time (just footsteps), but from Hyatt Place, the Toy Story Parking Lot is on the way anyway. I think if you go early enough, you won't have much of a wait in line or have to wait for the next bus because of crowds.