The public will always be asking questions about what they see so you need to know what is authentic and what is not. The main objective is to show the mosaic, to show the practical work involved in an ancient floor mosaic. It doesn’t matter if your workers all use hand made tools, wear handwoven tunics, or even if they are using hand quarried marble, it is the mosaic that counts. You can look more at authenticity in different areas as you go along but don’t make life too hard for yourself.
I’ve had people who want to find the original quarries for some of their material (some have been completely worked out and some have been lost to time, some we just don’t know where they are any more), remember the important thing is the mosaic and how you create it. Authenticity in materials is something you can improve on in time but initially, focus your efforts on getting something the public can see, and if anyone says ‘But has that marble been quarried by hand as the Romans did?’ then give them and pick axe and say, ‘Off you go’ (As a side note the Romans did actually have a water powered wet saw for cutting stone).
Work within your budget and time and you will still be able to create something that will draw in the visitors. Below I go through some of the areas that you can adapt.