He does sound sweet and odd, the kind of guy I would fall for too.
I think it is awesome that you are trying to stick it through his oddities. Sounds like this stuff troubles you and understandably so - his anxiety problems are getting in the way of how well he is treating you in this relationship. And I would have a hard time with a guy who would never perform oral. I work at an OCD clinic but I don't have all the answers. But I can give what I know. First of all, some of this sounds like it's related to his personality rather than his fears, like not calling you.. that doesn't sound like OCD. But the sex issues do sound like OCD, and obviously his checking stuff is OCD. And perhaps the needing to do laundry is also. Maybe he couldn't stop thinking about it until it was done. That is an OCD thing.

He actually sounds a lot like someone I know at the clinic.

Anyway, for you to work this out, you're going to have to find a way to talk to him about this stuff. Maybe his style of interpersonal communication makes it difficult to express your concerns. Could you write him a letter, expressing just one of your concerns at a time? I don't know, this kind of guy sounds like he would be receptive to a sweet, handwritten letter. Maybe you could just write about how you wish he would call more often? Or whichever thing you think you should bring up first. And then you couch it in sweet things to say about him or something poetry-ish maybe, or.. you know him. Don't make the letter all about the criticism is what I am saying. Also, choose this battle wisely. It will take him time to recover from any criticism like this, even if he doesn't show it. It will take him a LONG time to change his behavior (change from the norm is probably very difficult for him). And you should not ask for anything else from him that is different from his normal behavior for quite some time. He sounds pretty "walled off" not in the prickly way, but just in the.. reclusive, reserved way. Partly due to OCD, partly due to who he is. So little things will have to break down his barriers, and in the meantime, you will have to have enormous amounts of patience and the ability to be very subtle with him to try to get him to meet your needs without encroaching on his need for privacy and self-determination.

If he is very willing and very committed to your relationship, he may even consider couple's counseling. Is he in therapy? This also will help -- but it should be exposure and response prevention if it is OCD. ERP works better than medication for OCD. If the T doesn't do ERP, GO SOMEWHERE ELSE. Also, if you decide to suggest therapy to him, please do this VERY carefully!!

Hope this helps. And best of luck.