Hi, there! I'd love to help you with your question this evening. I am from a split home where my mother remarried somewhat quickly, so I have some personal experience with this. My stepfather asked that we (my brothers and I) begin prefixing his name with "Daddy" almost immediately. Although I now understand that this was his way of conveying love and his wholehearted intent to be a father to us, it created some awkwardness and resentment on our part, as we were all too aware that we still had a father, whom we saw on a regular basis. It also created some resentment with my father, if I recall correctly. For those reasons, I would not recommend pushing the kids to call you anything like "Mama --" until they are ready to do so. If you would like that kind of relationship and intimacy with them (as your children seem to have with their father) it does no harm to make the suggestion--just allow them to make the ultimate choice and take the lead on it.
I understand your values in appreciating a respectful "Ms." or "Mrs." in front of an adult's name. In this sort of relationship, it would place some distance between you and the children (establishing more of an authoritarian relationship, rather than the one you are striving for). You want them to feel close enough to you to trust you with their problems, want to talk things out, play with you, etc--therefore, a Ms. or Mrs. probably wouldn't work.
As far as nicknames, most of those are going to come from the personal relationship that develops between you and the kids. Sparky, for instance, because you light a fire under them in the morning and get them going. Bakerella because you're so awesome in the kitchen. Sugar because you love to give them kisses. Try to find something like that (that you're comfortable with) and enlist your boyfriend to help with making the nickname suggestion and getting it to stick.
Hope this helps! Please let me know if I can be of further assistance. :)