‘ulterior motive’ has a negative connotation. I think that thinking of yourself, while at the same time thinking of the other person is not at all a bad thing. Very balanced as a matter of fact.
You can split the thoughts if necessary: you really want the other person to get engaged.
Hashem, I really want to get engaged….
You are being mispalell for the other person as well as davening for yourself. Hopefully, by having the other person in mind you are building zchusim…