There is one more thing regarding MMS worth sharing:
I applied updates from here I am running modemmanager 1.22.0 (Byzantium is at 1.18.6) some time back.
Since applying the updates, there is some new behavior - If the data signal craps out, and I fail to receive an MMS during that time, I get a notification in Phosh stating that it failed to receive an MMS.
In all cases, flipping the HKS and waiting about a minute got me that missed MMS message.
(I am assuming it’s modemmanager at play here, but there may be other packages that were updated that provided this feature. Not fully sure :))