How can I prep a large amount of garlic quickly?

Have you considered ready prepared frozen garlic instead?
It's actually cheaper than fresh.

£2.75/kg from any supermarket.

Alternatively, if by 'Asian' you mean 'Indian' try garlic powder instead - that's the BIR [British Indian Restaurant] standard. Approx £8/kg, but of course it goes a lot further than the same weight in fresh/frozen.

If you're dealing in wholesale quantities, then you can get ready-peeled, fresh, but it's the most expensive option, and the hardest to look after if you're not going to be using the whole lot at once.

As already mentioned, serving garlic skin will not endear you to your customers.

In the UK, you can get the following types, in order of how much like garlic they actually taste.
Fresh
Fresh, peeled
Frozen, peeled
Frozen, crushed
Frozen, purée
Dried, powdered
Canned [or jar] peeled
Canned [or jar or tube] purée

Of these, you'll hardly spot the difference between fresh & frozen, whole or crushed. Purée is a little milder but still tastes like actual garlic. Canned doesn't work for me at all, it's lost all its 'edge'. …and note I put powdered above canned for taste.
Frozen crushed is almost impossible to tell from fresh, but is expensive; a bit of a supermarket premium product. Frozen purée is very cheap & very versatile. With frozen, if I'm cooking it I'll use purée, if it's going to be raw or dropped very late in cooking, I'll use crushed.
[I've never seen fresh, peeled in supermarkets, only from wholesalers, the rest you can buy just about anywhere in the UK]

If you have dough kneading machine (or any of that type) just cut top and bottom from garlic heads, throw the cloves in the bowl and turn the machine on (with and ending that have the most "stirring" ability). Then just sif the skin from garlic itself. Pros - only work needed is to cut the heads in a way that also cut tops and bottoms of cloves. Machine do the rest while for how long you want while you do other things.

There is also method (but in my opinion more effort consuming). Crush each head (bettwen two cutting board for example). Put cloves aside and cut their steams off. Then crush them lighly again and the skin can be easily removed.

After you have loosened the peels by some method, you can get rid of the peels by winnowing, the traditional method of separating grain from chaff. This method requires:

• a wide bowl or basket to hold the garlic
• access to outdoors
• a stiff breeze
• reasonable hand-eye coordination
• an outdoor area where leaving garlic peel scattered on the ground will not be considered littering

Take the bowl of garlic outside and toss the garlic up into the air, then catch it in the bowl again. The breeze will carry away the loose peels, while the cloves will fall down into the bowl. Repeat several times, until most of the peels are gone.

If you don't have a stiff breeze, you could use a fan, or have a partner wave a large baking sheet to create breeze. But don't try this indoors; the time you spend cleaning up the scattered garlic peel will eat up all the time you saved from not picking the cloves out by hand.

Roasting garlic is easy, gives a better flavor in many cases, and makes it super easy to remove the peel. It can even be done in the microwave very easily. Once you roast it, you can either squeeze the cloves out one by one (it will come out very quickly), or you can use a paring knife to remove them, whichever is easier for you - either way it will be much, much easier than peeling raw garlic.

The flavor will change, of course; roast garlic loses some of the sharpness and instead has a more well rounded, mellow flavor, so it won't fit in every dish - but many stir fry dishes (especially beef) work well with it.

For the peeling, just take the whole clove, crush it with the side of a knife or some other flat object, and you can pick the peel off in one piece. I couldn't believe it until I tried it myself, but it really works extremely well.

For the mincing, I'd just use a food processor and watch it carefully to get the right size and not make a puree.

Why not just use a garlic press? This removes the need to peel the garlic beforehand and if the hole becomes clogged with garlic skin you just dump it out and continue pumping out garlic?