Vilvam can be offered to Perumal. It is known that it will not be a misdemeanor since ‘bilva nilaiyAya namaH’ is towards Thayar. So it can be offered to Perumal. Because offering Vilvam to Shivan is considered special, they do so.
The question itself mentions that Vilvam leaves are offered to Srinivasa Perumal at Thirumala during Dhanur maasam. Hence it means that Vilvam can be offered to Perumal. What is the special reason that it is only offered during Dhanur maasam at Thirumala must be queried around. Whatever the reason, Vilvam can be offered, and let us accept that it can be offered during the Dhanur maasam.
Since Pongal is generally offered during the Dhanur masa aradhanam, and because it is a salted preparation, parishesanam is not applicable for that. Without parishesanam, Pongal can be offered after shosanam and plavanam as purificatory rites.
There is an ancient Sannidhi for Dhanvantari at Srirangam temple. In that Sannidhi, Dhanvantari Jayanthi is celebrated during the month of Aippasi and on Hasta nakshatram. We can follow the same.
Srivaishnava-s need to perform any aradhanam, japam, dhanam, etc. that is mentioned in the vyatIpAtayogam. It includes several karma-s for material benefits (kAmya karmA). We have been told not to perform any rituals for material benefit.
Adiyen is not aware of where the shloka that starts with ‘vyatIpAta mahAstava’ is. Many meanings can be said for ‘vyatIpAta’ – it could also mean ‘One who transcends everything’. Maybe because of this meaning the association could be construed. It would be convenient for adiyen if you could point out whether it is vyatipAt1a or vyatipAd3a in the shloka. Adiyen is also asking several others about this.
Usually, one must not partake food before tharpanam; tharpanam must be done only on the day of masa pirappau. The following day is not a punya kalam. Because of this, if one is unable to wait until the appropriate time for masa pirappu tharpanam, one could do the tharpanam a little earlier and partake food. Even if this is not possible, as asked in the question, one must avoid performing tharpanam after partaking food or the following day.