"The entrance song ... is to open the celebration, deepen the unity of the people, introduce them to the mystery of the season or feast, and accompany the procession."

"The procession with the gifts is accompanied by the offertory song which continues at least until the gifts are placed on the altar."  Consider not having a song during the preparation of the gifts.   If you have able instrumentalists then a season when instrumental music quietly accompanies the preparation of the gifts can be quite powerful.   Perhaps during Lent and Advent you might consider gently singing a chant with no accompaniment at all - just to heighten the atmosphere and focus peoples' attention on what is happening at the altar.

"...after communion ... An antiphon from the Roman Gradual, with or without the psalm, an antiphon with a psalm from the simple Gradual, or another suitable song approved by the conference of bishops may be used."   Just think about the people - what do they need at this point - space to pray privately or an opportunity to join together in song?

There is no mention of an exit hymn in my Missal - the dismissal concludes the Mass.   There is a phrase that might help, though ...