From a son-to-be ordained deacon:
Many years ago, as I was beginning in seminary, I made a private vow to the Blessed Virgin that I would offer the first liturgically free Mass in her honor if she would help me to persevere to priestly ordination. She has admirably answered my prayer and now it will soon be time to uphold my end. However, since I am to be ordained on the 26th of May, [A fine day to be ordained!] the Monday will not be liturgically free for a IV class Votive Mass of the BVM (obviously, Sunday is not). So, the question is, how would you recommend that I fulfill this vow? Is there some exception of which I am unaware for the new priest’s first three Masses (which are meant to be said for special intentions: thanksgiving, in honor of the BVM, and for the dead (of the family), right?)?
It would be my strong desire to fulfill this vow in the extraordinary form. However, if it is simply impossible in the EF, ought I then to do so in the OF on Monday, which would indeed be free.
There is indeed a tradition for a new priest to say votive Masses in the manner you mention. I have heard different versions. But I warmly approve of a votive Mass of the Blessed Virgin, especially given your promise.
First, you said that you said “first liturgically free Mass in her honor”. Therefore, I am not sure what the problem is. You are free to wait for a day that you know, for sure, is free!
However, if you want it on a certain date because of circumstances (family is still around, choir is available) you can always ask the local bishop for permission… if, that is, the bishop would not look askance at such a request and, therefore you. He will probably be benign (and slightly amused) and paternal.
Otherwise, given the particular situation (and few situations would be more particular given that priests are usually ordained only once) and that you are talking about ad hoc Masses, I think you could just do it anyway. These matters of the calendar are, I believe, pretty flexible.