I think that if you spend some research time, you can find various things to do to keep power drain to a minimum. I keep my phone "on" with screen off all day on long trips, and find that one or two conventional batteries do it between town stops. That plus being alert to opportunities to recharge and not using the phone for things you don't really need to --- that makes it work out fine for me.

On a previous phone I got a couple of those fatter extended batteries that required replacing the back plate on the phone. They were less expensive than what you're talking about, made in Asia somewhere by a third party and worked okay. There can be gotcha's with that approach as I recall; I think one mount or charger or something would no longer fit the phone, and a case I had for the phone no longer fit it. The replacement back plate was a PITA to get to click firmly and reliably into place --- an artifact of coming from a third-party no doubt. Indeed it is nice, however, when in a trail town to be able to plug the phone in somewhere and forget it for a while and the result is that you end up with more charge. And then on trail not having to power down and swap batteries as often (or ever).

I wonder if the issue here is how (and how often) you use the GPS? I can't imagine just leaving the GPS on, unless for a moderate period of real trail confusion, or on a day hike where power wasn't an issue. For me, at least, a GPS on a cell phone is good for infrequently getting a "where am I right now" fix and then turning it off.

On thru-hikes, I use my phone most often as a camera and to type up a journal entry at the end of each day. Very infrequent use as a GPS, as a telephone, not quite as infrequent use to get a weather report or upload journal entries (text only while on trail). Once in a while as a voice recorder. Almost never to read books (exception: hiking in late Oct or Nov).

I imagine that the particular model phone you have makes a difference too, but just figuring out what sort of background processes are sucking up battery power is worth some time before doing a long trip IMO.