Perhaps a silly question - how does the host bread used by Byzantine Churches (and most others) fit into the Latin Monstrance for said procession?

The monstrance has a "lunette" adapted to hold a piece of the cube-shaped Lamb.

Only if you subject the Holy Lamb to such manhandling as would have done the Mexican Revolutionaries proud!

I found more photos from the Eparchy of Mukachevo website of a Eucharistic procession for the Feast of the Most Holy Eucharist in 2010.

Three photos in particular contain close-ups of the monstrance with the adapted lunette (you can click on each to enlarge further):
Photo One , Photo Two , Photo Three

My concern is the amount of particles that can be generated from placing the Holy Lamb into the lunette.

Then, there is this photo from a parish Eucharistic procession in which the Holy Lamb appears reddish in color (moistened with the Precious Blood obviously). I am presuming the Lamb was allowed to dry previously or else it would have been a disaster to place It into the monstrance.

Another reason to not celebrate this purely Latin feast. If one wants to go and celebrate it with the Latins, fine.

In my purely layman's opinion, we run into trouble not so much for practicing Latin devotions and celebrating Latin feasts, but from neglecting and ignoring our own. For instance when I started attending a UGCC as a teenager we never had Liturgy of the Presanctified Gifts in Great Lent. My current pastor didn't either growing up in the 50's and 60's in Pennsylvania. He said they just had "Stations of the Cross". Now, thank God we have the option of celebrating our own services as well as the resources to do it (i.e. service books in English).

Now I'd have to say that here everyone who would attend Stations also supported the Presanctified Liturgy, although some parishioners were concerned that the Presanctified Liturgy didn't focus enough on the "sufferings of Christ".

Best wishes to everyone!
Stefan-Ivan

Another option to help with "Stations withdrawal" that I have found helpful, especially when Presanctified is not celebrated, is to celebrate the Akathist to the Passion. It is beautiful, within the tradtion and was composed by St. Innokenty of Kherson and Odessa.