Luckily I only experienced one night of my h 'bed clinging'. If he was any further away in the bed he would have been in the bathroom - that was the night before he dropped the bomb. It is horrible so I know how uncomfortable it can be.
I know your goal is to have your wife back in your bed with you but maybe you should break it down. After all having an unwilling wife is not doing you or her any good. I don't think you should give up or accept that it is just easier this way, I think you need to set some smaller, bite-sized goals to make both you and her feel more comfortable around each other.
I think the major one is your bedroom and you have done an AMAZING job there. Can you come and do mine?? What other things can you do to make her feel more comfortable. Maybe more of the the 'can I get you anything?' question when she and s were on the couch, that showed thoughtfulness and she responded well. Also the loving, kind words that were in your letter. Are you warm or cold when you speak to her? Does she feel 'cared for' in words as well as actions?
I know it is really difficult when you get no response but these things broke the ice a little. Can you take them a step further or increase them?