Gravity Bleeding (Never Heard of it) by just opening up the bleeder valves, would seem to me to be extremely likely to introduce air into the system. Throw in, how uncommon it is, pretty much confirms it probably doesn't work that well.
Like mentioned, if your stuck doing the job yourself, speed bleeders can be found at your local auto store for about $10 an axle, in the "HELP" section. Take your old bleeder valves with you to find the right size. They are bleeder valves, except with one-way check valves in them and thread sealant on the threads, when you open them, they let the fluid out but won't allow backflow for air to flow in.
Rear Drums way out of adjustment can make the brake pedal seem mushy, actually its called pedal height, out-of-adjustment rear drums require you to press the brake pedal down really far to move the shoes out until they contact the drum, the pedal won't produce much resistance till than, nor will any brake pressure build and provide any brake force to all 4 wheels. Adjust the rear drums properly, pressing down the brake pedal will cause the rear shoes to contact the rear drum immediately and the pressure builds right away and provides brakes much sooner, HIGHER PEDAL HEIGHT.
Changing shoes and then using the self-adjusters to adjust them, is NOT a great idea. The rear axle is already up on jackstands, the toughest part of the job, if you changing shoes, is already done for you, might as well take a few minutes to manually adjust them and make sure its done right.
The self-adjusters are the most likely thing in the rear drums to fail first. As well, I've seen perfectly good self-adjusters NOT work when the shoes were way way out of adjustment, like when you change out new shoes. The ridge that often is present from the wear on the drums forces you too adjust the shoes inward a lot to clear the ridge, you don't adjust them manually, it may take a long while before the self-adjuster move those shoes out to take up the slack, if at all.
I'd put your vehicle's rear axle back up on jack stands and check the adjustment of the rear drums, the tire should spin with only the slightest drag from the drum brakes, and adjust them manually if necessary. Then bleed the brakes again, get the speed bleeders if you need to do the job yourself.