There is no such thing as "quick" anything at WDW. If you plan on doing this, I would highly recommend taking an uber/lyft/cab at the very least to Poly from All Stars. If you rely on Disney transportation, it could take you up to 90 minutes just to get from your resort to Poly.
The parade is at 3:00 pm. If you see it from Frontierland/Liberty Square, it will be over by about 3:25 pm, but then you have to walk all the way to the MK entrance. If you watch it along Main St. or near the entrance, it won't be over until about 3:45 pm. You then need to walk to the bus, wait for the bus and go back to your resort. If you are lucky, you'll be back at your resort by 4:30 pm. Personally, I would be getting into a cab/uber/lyft by 6:30/6:45 pm to get to Poly at attempt Tambu so you can be at the monorail station by 8:15 pm at the very latest (even earlier if you want a better spot for HEA). It will most likely be very crowded and chaotic up there. If it's really bad, I would step up to the bar and get the Lapu Lapu's and head down to Capt. Cooks to get some actual food.
Personally, if you can skip going back to the resort and just find some relaxing things to do in the MK resort area, I would do that. Take a boat to WL and relax in the lobby, head out to Geyser Point for a drink and just chill out there (It's really lovely). Or do a monorail tour and go to Poly earlier (Trader Sam's opens at 4 pm and it's super fun in there. They have great apps as well.)