I've seen some of your posts around and dang, it sounds kind of rough to find something for you. I personally would never think about even trying to do the majority of my PbP gaming via phone, for the reasons you've just mentioned. Not being able to look up mechanics or campaign notes easily while typing up a post would be ahuge hassle for me, and being unable to edit my posts easily as I write them would make them a pain to write.
I suppose the best thing I can recommend for you is to memorize the mechanics about your character you'll need to know on a regular basic. Ability scores, which skills you are proficient in, to-hit and the damage of your weapons. Though that only is band-aid on the problem for you, I think.
Maybe what you want is a diceless system? Those are certainly out there, though they tend to be more on the obscure side. Freeform Roleplay might work for you. It places a lot more responsibility on your shoulders as you have to decide what your character is capable of doing, since it involves no dice or mechanics, and it requires a lot more roleplaying on your part, but you'll still often see other players who run longer-lasting story-archs where they essentially take on the role of a GM, and write up small adventures for other players to explore. Heck, I'd be kinda interested to see someone try to get a freeform dungeon crawling game going.
From glancing over the basic rules, this looks pretty interesting and solid. I especially love the idea of competencies, since those sound like they really allow for some huge increases in character power over the course of a campaign. That's a really clever, elegant way of going about that. I'll definitely keep an eye out for the finished version.
That said, I'm not to sure about the fact that players need to make checks to defend themselves. I've faced this sort of issue with saving throws in D&D before, and in that case I've solved it by rolling for my players and having them roll for me, and also rolling for any potential damage in advance. That would work for attacks here as well. But I'm not entirely sure about complications. From what it sounds like, the player needs to come up with a way for his character to get through them, and then roll the relevant Ability check? That does sound like it'd require me to approve every attempt to overcome complications personally, as I'd have to decide what course of action is or is not appropriate. Or do I as the director set down in advance what checks can be used to overcome a complication?