Good one. I think you could probably pull it off. I've seen it done before.
With that said, some clients, psychologically, will need to talk out their problems out loud. They may even tell you that. It's how they need to operate. They may just be too much for you and that shouldn't prevent you from doing well at your business with other clients.
This would tend to be especially true if you can make it clear that you are running a business (sole proprietor) and text-only is your business policy. You could probably even address any issues in a reasonably cool way without talking about your personal health conditions which is kind of a no-no for anybody involved where typical business boundaries are concerned.
So a big part of this might be developing the vocabulary to talk about it at a level that meets the needs of prospective clients and also says, "We can talk about it ALL you want but my boundaries are right here, and I'm also ready to help you out with stuff I'm good at."
Eventually you may also find some related vocabulary for navigating phone calls in a way that makes it clear you are not there to give a half-assed solution over the phone, so you'll need some time. For example, "let me take a look, I will get that on the schedule," "This is new to me, so I'll have to think about that, let me see how the schedule looks," etc.
It may help to think of you as the business, and write about the "you" problems from a third-person perspective. What will you have the business owner do about the issue, if they're your video game character? This can help you focus more on strengths and less about what you can't do for people. It does sound like you have plenty of talent for what the typical small-biz web development client would need.
Getting into a couple of other specifics--if you can, it's a good idea to establish a plan for frequency of communication during a project, and communicate that you have such a plan, up front. "I'll expect to reach out with updates at the next milestone, which is X on date Y. If you have any questions between now and then, my contact information is below." This will also help your clients to be more comfortable not using the phone, since they know their info-needs will be taken care of in any case. You are basically soothing them, so to speak.
It's also a really good idea to practice and develop professional use of your favored media as a way to avoid inadvertently raising the stakes via text communication. This could include using a professional email signature which invites people to reach out (any of these text-based methods). Also, writing emails that do not seem personal in nature and clarifying things to avoid misunderstandings.
Good luck, like I said I've seen it done and if you can develop your practice over time you might even find you get in good with one or two clients, they really love your work, they also like text, and you're set. I think it would be reasonable to look forward to outcomes like that for sure.