Lou, in my limited experience, I would think that your H is trying to establish a normal facade for your relationship - mine was desperate to make it look as if we had both agreed that he should simply walk out on his family and take up with OW. He needed it to look like I and the kids were OK with his behaviour.
It was so bizarre - we ended up feeling like we were going mad.
My guess is that mlcers really need to make it look to the outside world that they are good guys.
It's Ok if this helps you deal with him/the situation, but please don't think that it is a sign of him softening towards you, or that he is moving towards wanting to come back at some time in the future. My guess is that it's still all about him.
And re how you sign off - again, ny experience is that whatever you do in this regard will have no influence on his realisation that you are leaving the door ajar.
To use familiar terms/names from our previous relationship with them tends to make us look weak and needy. These guys have walked out; they have re-placed us. They are not our H's anymore so we should not act towards them in any way that suggests we still think they are. It's pursuit, and pursuit does not work.
Sorry to be so negative, and just my 2c. But I have made just about every mistake it's possible to make, looking back.