Recommendation and opinions vary widely.
Everyone's process is subtly different. but there are some constants:
- Curd must let go of all whey along its microfissures. It's fine if the curd has stable water incorporated in its matrix. It's not fine if there are residual whey pockets. Whey pockets are caused by: uneven curd size, uneven stir schedule, heat gradients in the vat, heat gradients during press, pH gradients, bacterial flocculation leading to uneven distribution, improper brining where surfaces do not get even exposure, etc. Mostly, though, it's the uneven curd size or mismatching the curd size to the flocculation multiplier and milk type (this is why most cheeses are 3/8" curd with a floc of 3x)
-Slight rind must form in the sense that it can't be wet. Typically coincides with #1. Rind drying is accomplished naturally in most cases by resting wheels for a day after brining.
- Milk quality is drastically different among makers, so are cultures. Cultures that offgas tend to not do quite as well when vac packed.
I see many commercial operations vacuum pack their Cheddar and Colby right out of the molds.
Yes, because the moisture is rather low (37% ish), and the huge press for cheddar dries it out, no whey left.
Cheddar, Colby, and Parmesan can all be Vacuum packed after a day if they are made and pressed correctly?
Yes. Typically, below 38% moisture, you can get away with it. Above, it requires a bit of kajigerring, like aging at lower temps.
They do not need any oxygen in or need to allow any waste gases out to age properly?
No, they'll be fine. But typically for vac bag aging, you can't do it quickly. You need to keep them at 40-48F.
Your saying the most important thing is basically the moisture content?
Whey pockets, actually (process control). Then moisture content (cheese style).