I don't think that many did really understand what your question was about, but you ask what is the best method to stabilize the footage while walking?
Gimbal is the best solution, but ninja-walking is the only solution to get stable footage with/without gimbal.
I do not do Portrait mode is that what you're asking
a gimble will not get the bobble walk out , as I still get that if walking with one, and I would have to go 1/4 speed ahead to minimize it
maybe a video would help, DJI here rest assure your topic will get help from others, and offer minimal help
To keep the horizon straight, indeed a gimbal is really the only way. The trouble is that once you have used a device with built-in horizon levelling, anything else seems crude. It's a pity that the Action does not even have an on-screen indication of level horizon. I rarely use my Action because of this. I do have a DJI phone gimbal device which can accept the Action with an adapter, but then the whole thing seems rather large compared with my Pocket 2.