Hellooo! Will try to be of help as much as possible and as mentioned would love input from others. A great source for this period is Maurice's Strategikon (trans. George Dennis 1984), which was likely written at some point from 575-628 AD but can be taken as a general indication of what was going on during the 6th Century AD. It suggests the following for cavalry...

"They should have hooded coats of [scale, chain, or lamellar] mail reaching to their ankles, which can be caught up by thongs and rings, along with carrying cases; helmets with small plumes on top; bows suited to the strength of each man... cavalry lances of the Avar type with leather thongs in the middle of the shaft and with pennons; swords; round neck pieces of the Avar type made with linen fringes outside and wool inside. Young foreigners unskilled with the bow should have lances and shields. It is not a bad idea for the bucellary troops to make use of iron gauntlets and small tassels hanging from the back straps and the breast straps of the horses, as well as small pennons hanging from their own shoulders over the coats of mail... Apart from the foreigners, all the younger Romans up to the age of forty must definitely be required to possess bow and quiver, whether they be expert archers or just average. They should possess two lances so as to have a spare at hand in case the first one misses. Unskilled men should use lighter bows. Given enough time, even those who do not know how to shoot will learn, for it is essential that they do so. The horses, especially those of the officers and the other special troops, in particular those in the front ranks of the battle line, should have protective pieces of iron armor about their heads and breast plates of iron or felt, or else breast and neck coverings such as the Avars use."

...and for the infantry...

"The infantry soldiers should wear either Gothic tunics coming down to their knees or short ones split up the sides. They should have Gothic shoes with thick soles, broad toes, plain stitching, and fastened with no more than two clasps; the soles should be studded with a few small nails for greater durability. Boots or greaves are not required, for they are unsuitable for marching and, if worn, slow one down. Their mantles should be simple, not like the Bulgarian cloaks. Their hair should be cut short, and it is better if it is not allowed to grow long" (Dennis 1984, 12, 138).

Long story short is in my opinion they can be fudged into an Early Byzantine army, but are not ideal. The lack of composite bow cavalry archers and suitable auxiliaries such as Avars, Bulgars, Ostrogoths, etc. would be the biggest problems in my view, although the lack of lamellar armour (as compared to scale and mail) would also be notable especially as the 6th century went along. But it highly depends on the specific campaign in question, as there was a pretty big series of visual changes from the Constantinian Roman of the early 300s to the tagma that existed by the 700s AD. Interested to see what Linear-A does, as they appear to be targeting Justinian's mid-6th Century AD army with a couple of their future sets.