I think you're doing wonderfully well. You're being honest, age appropriate, and compassionate to your DD1, who could ask for more than that?
The problem is you have father who is undermining everything you are doing. And TBH there's probably not much you can do about it. You aren't going to change him and you should never 'grill' DD about 'what Daddy says' (I know, you aren't). The most you could do is, if she says anything about 'Daddy is sad' or 'Daddy is lonely', simply ask her "Oh, why do you say that?" and then listen. I have a feeling you'll find out he's playing on her emotions and possibly even saying some 'negative' things about you. Write them down, but do not pursue followup questions. Simply do as you have been doing, reassure her and gently 'correct' anything he's told her. I think your line about Daddy enjoying some 'me time' is a good one. You can also say that grownups can find things to do to make them not feel lonely and you're sure that Daddy is doing that.
I said to write the things she says down because there is such a thing as parental alienation. If his 'I'm lonely' crosses over into him saying negative things about you, severely playing on DD's emotions, or saying that the break up is 'your fault', that is something to speak to your solicitor about. A parent is not allowed to say negative things about the other parent. Judges do NOT look favourably on that! And repeatedly playing on a child's emotions about how much a parent is missing them and how lonely they are without them is not looked on favourably, either.
My advice is do not show him those post-its. Those are DD's private thoughts and, as upsetting as they are, not yours to share. Besides, they aren't going to change his behaviour one whit and you're right, they must might give him 'emotional ammo' to use with DD. I'd take pictures of them, then leave them be.
I think your idea of getting counseling for DD is a good one. You could explain to her that it's so she has someone she can tell everything to who will not share her 'secrets' and she doesn't have to worry about hurting their feelings.