Any preferences/opinions/insights as to what to use? ... We'd like to go with phones if possible instead of adding another piece of gear.
All the thoughts above are good.
I spent a couple months doing the GDMBR this summer past. In addition to paper maps, ACA phone app on my Samsung Note 8, and ACA GPS on my small-screen, Garmin Etrex 22x, I also carried a small Surface Go2 tablet.
I used them all for different purposes. The Etrex 22x kept me on track. En route, the phone came out to update me on estimated distances and travel times to various services. In towns or crossroads with cell signals, I'd take the phone out of battery-saving airplane mode to click and make calls directly to businesses listed in the ACA app. The big maps were great at the beginning and end of the day to review the big picture, which somehow, always sticks in my mind better when using big paper. The computer/tablet also provided additional mapping capabilities, but a free state highway map might have done the same thing for about the same weight. For one of the updates to avoid logging, I used by RWGPS and a direct download to the Garmin. My preference was for the Garmin, but I could have gone either way.
Did I have a preference at the end of the trip? Well..., no.
If I had to pick only one, then I would still go with paper - less risk of malfunction.
If I was in a hurry (as you will likely be with an August departure) and had to shed weight, I'd probably go with the GPS, using paper as a back-up.
We all feel the need to carry a phone - so I'd have no problem using the ACA app in navigation mode on my phone as primary - and have done so on road trips (such as the Lewis and Clark) with the phone firmly attached to my stem with a motorcycle-quality mount.... Hobbes' comments on problems mounting a phone for the GDMBR are on the money. Presumably, once shock-proof phone-mounting systems improve, Frontpack improves the platform for ACA maps, and power management for phones improve, we'll all be using the ACA phone app. Right now - not quite ready for prime-time in the back country.