As your DD is 8, does she ever get invited for sleepovers, after school activities, weekend commitments etc?
I would perhaps pish back slightly/spread out the suggested dates with godfather with - sorry she has a sleepover, perhaps the following weekend? Or that weekend is really busy with a gymnastics tournament and the following is tied up with her best friend's party, so the weekend of the ?5th is free, would that suit?
Or simply, she's not free this weekend or next, how about the weekend of the ?5th. Not a big deal in spacing his visits to every 3 months, or once a month, or whatever, just working in with family commitments.
If they are suggesting weeknights, I'd be less happy with tired grumpy DD midweek, but if it were done at a reasonable hour etc, might be OK. Maybe alternate weekend one month, weekday another month.
I think it's great he wants a relationship with her, because as she reaches these teen years, having an outside person to stabilise things can be a great idea.
I know you say you move around and i can relate, but is there a neighbour/friend that can be called upon to bestow a similar treat on the younger two, preferably on a different day to eldest DD, so sometimes she "misses out"?