I am a HUGE proponent of self-insuring for roadside issues and not paying a 3rd party company to take their profit on top of it.
So I use my phone, and a credit card. I have needed one tow in the past 25 years and it was a whopper...I paid almost $600 to get my truck and trailer out of a ditch in a serious stuck situation in the middle of the wilderness, hours from the nearest tow company. He spent a solid 2 hours prying my truck and trailer from the woods with his $400,000 truck, damage free, and he drove 70 miles one way to reach me. And I paid his asking price for that service out of pocket, and happily.
Get in a bind? Clear your head, stay calm, Google a local tow company, tell them you'll pay on the spot with a card or better yet cash, and they will rush to your assistance...because the low rates they get from AAA and HondaCare and whoever, are less profitable than private tows. While they service you, the AAA and other subscribers can wait. I dealt heavily with this in my insurance career (many insurance companies offer this service also for a fee) -- this prioritization of private payers is very real. Private payers almost always get first service over any other subscription/contract tows...which is important during big ice storms and such when the network is overwhelmed. Money talks, and AAA and others are always trying to beat down prices. But when I'm in a bind, I won't negotiate. I'll pay.
So in 25 years I've paid $600 for one nasty incident. $24/year. Beats AAA!
I'd give Honda Roadside assistance a shot if it would benefit me, cuz under warranty it's free. But it is so incredibly easy to handle this stuff yourself with today's cell phones and coverage, I'm surprised so many people still use AAA and other such services in the modern world.
Lockouts, lost key coverage, gas deliveries, all that stuff...no use for me cuz I'm not that flaky lol! And if I DO flake someday...cuz I'm not perfect? I'll pay someone to bail me out ONE time...and I'll save money over the long haul.
I will bring up one dark spot in your scenario (and it's quite an individual one): I every instance where we have needed a tow in the past 10 years we were someplace where there was NO cellular data service. If we did not not know a phone number we could not contact anyone. It's in cases such as this that having one number to call is helpful.