You could stop doing the chore things together -- walking the dog, going to the gym, making food, studying on the couch, etc -- and do it APART. Seek out other friends and people to to that stuff with. A dog walking group or gym class pals. Whatever.
Then you can spend your "together time" on the romance stuff that you crave more of. Instead of spending it on the mundane things of living.
If you are cooped up with each other all the time it get cabin fever-y because there is NOTHING NEW to talk about. Wanting more time/attention when he doesn't have it to give -- he gets tired and then you perceive it as pulling away and maybe act in hmmphy ways, which turns him off and leads to no sex intimacy, which hmmphs you further -- it becomes this spiral thing.
As for your conflict resolution style
-- could you work on that so you don't get anxious by that and stop being avoidy? Then he can share his vulnerable more with you instead of walking on egg shells worrying you are going wig out.
Emotional intimacy can lead to other kinds of intimacies. Then you are helping yourself to feed your "I am secure" bucket and not your "I am anxious!" bucket.
Confidence is grown by doing -- so you have to open yourself to risk and face conflict more directly to learn that -- "Hey! I can handle this! And I didn't wig out too badly here and nobody broke up! Whew!" and then next time you don't have to feel so anxious. You have direct experience telling you that you CAN handle this. Then you are working toward being more secure in yourself.
Could that help any?