Late Roman Unit Sizes

[Renatus]

Hypothetically, if I decided to define the units of the Lanciarii and Mattiarii as light armed infantry, could I get away with calling the heavy infantry scutati?

I think so, yes. That is the sense in which I read Vegetius' use of the term. I would be careful about categorising the Mattiarii as light infantry, although their association with the Lanciarii suggests as much. We don't know what the mattium was, as far as I am aware. Personally, I do not think that it is the same as the mattiobarbulis but others may disagree.

I do not run with your idea of the Lanciarii fighting at close-quarters like the old hastati. Depictions of lanciarii on tombstones show them holding a clutch of javelins, which suggests to me that their role was to stand back and put down a barrage of missiles over the heads of the line infantry. Scutati seems much more descriptive of troops fighting in the line.