Would the Mass viii agnus fit thematically with your Mass? I believe that is the appointed Mass for Christmas, according to the liber.

I think we all need to lighten up a bit and look at the music first. It isn't necessary to infringe on the hard and fast rubrics or do anything uncanonical to make these masses work.

The way we always do these is to sing the polyphonic setting that has 'miserere nobis' first, sing the second Agnus in chant, and then the last one (polyphonic with 'dona nobis pacem') at the end.

It isn't necessary or even desirable to get really literal with the suggestions in the Liber about which ordinaries are for Christmas, duplex feasts, etc. etc. As mentioned many times before in this forum by people much more authoritative than myself, those designations are just suggestions, not rubrics. The various parts of the ordinary were first grouped together like this by the scholars at Solesmes. In the original documents, most (if not all of them) were just individual mass parts in the manuscripts where they were found. To use these polyphonic works successfully, practicality must trump non-essential considerations. (The result will still be canonical!)

First, look at your polyphonic mass and see what mode the polyphonic Agnus Dei is in, then choose a chant Agnus Dei in that mode. We always use the middle Agnus of any given chant mass since that is what is generally missing in the polyphony. Of course, if you wish to substitute the first Agnus with chant, that's fine too - whichever way you want. If you are using a pre-Trent mass, then you do have to do some editing to make it fit the Tridentine liturgy, but Hassler should be fine just using a chant Agnus to fill in. If the Hassler is in Mode 8, then Mass VIII (also Mode 8) will work just fine. (Sorry, I am not familiar with that particular Hassler mass.)

The Agnus Dei is in the same place as chant - all you are doing is using polyphony instead of chant to sing the canonical text. The only time the rubrics change is when you are singing a chant Sanctus - then the Benedictus is sung contiguously with the Sanctus (as in OF masses), whereas if you are singing a polyphonic ordinary, you stop after the first Hosanna and wait until after the consecration to sing the Benedictus with its Hosanna.

I hope this helps somewhat.

I think I'm also singing that same mass for Advent IV.

Listening to it on YouTube, you could use Agnus Dei XVIII or Ad Libitum II and they would both work well. I don't know what our choirmaster is planning, but I rather suspect that he's going with Ad Libitum II.

We did indeed use Ad Libitum II for this mass.

The point of the Ad Libitum chants is that they can be used in any season.