Best caliber for goats?

You cant supply a commercial restaurant, there are regulations that need to be meet for processing meat for public sale. But you can ask them them about if they know anyone who might be interested on individual level, or for pet food.
As for grain weight that would be like me telling you what pellet to use for your air rifle. I have no idea what will suit your gun, the distance you'll be shooting, or the effect your after on impact. You will have to sort that out yourself. Projectile testing is something you seem to like doing so shouldn't be a problem for you.

Latest update on the goat culling saga...

Went south again last weekend to the same horse property.
This time I took Little Emma (.177 air rifle, 22FPE), my new unblooded Tikka .17HMR and a .308.

First time out using (culling with) a .17HMR, and I must say, it is a fun gun of note. I was very pleased with its performance. I've zeroed it at 115yards, and its pretty much point and shoot from 20yards out to 140ish, and not much drop out to 200yards.

I again didnt find any deer, so it was just the .17's that got some trigger time this weekend.
The pest control (culling) tally for the weekend was:
4 goats
18 turkeys
9 rabbits
6 hedgehogs
4 mice
2 hares
and a possum.

The .17HMR was responsible for the 4 goats and 18 turkeys, Little Emma took the rest.

So my impressions of the .17HMR after this weekend are as follows...
Having only just started using it, I still need to work out my limits and comfort zones using it, but I was shooting the 20gr CCI game point, which is not a frangible varmint bullet, it is supposed to be a hollow point which mushrooms, holds together, retains its weight and penetrates to the best of its little 20gr ability. (which is certainly impressive, I must say!)

The turkeys at 70 to 100 yards were no problem. A turkey is a big bird, but that tiny 20gr .177cal bullet made short work of them, from any angle, usually (with out a lot of investigating) exiting. I didnt have time to do the dissections I would have liked to do in order to gauge terminal ballistic performance, but it was impressive none the less.
One of the flocks of turkeys I came across was a flock of 8 birds on a small flat high up in the hills. The wind was in my favour and they were slightly up hill of me, so as I peered over the chest of the track I was on I could see them, but my body was hidden from them below the rise. An almost perfect situation. I was about 70 or 80 yards away and managed to cull the entire flock with some fairly quick shooting.

Its performance on the goats was even more impressive.
The first goat was a steep downhill shot at about 30yards. Back of the head and it dropped like a stone.
Bullet exited through the eye socket.

Second goat was also a steep down hill shot, maybe around 90 yards with a lot of tree branches in the way. I was looking down a fence line and had a small window clear of vegetation and all I could do was watch the mob of about 20plus goats walk through the little gap I had to shoot through as they were ducking under the fence into the native bush. Eventually one stopped in the window, I could see a chest shot and I took it just behind the front leg.

The third and 4th goats were on a huge open paddock, again from a mob of 25plus goats. (no shortage of goats there and the owners want them gone).
Not much cover to make an approach, so half the mob was aware of me as I took up a position and set up my shooting sticks. I chose to go for a neck shot at 106 yards on a full grown nanny who was not aware of me and still feeding. She dropped on the spot but did require a coup de grace. Necropsy revealed the bullet hit and broke the bottom edge of the lower neck vertebra.
4th goat was a young billy, I didnt have time to range it but it was around 130 or 140 yards. Quartering away shot, just behind the shoulder, was also a vertebra shot as it also dropped on the spot.

Every caliber has its merits and its limits, and with more use I'll figure out where I'm comfortable using this little tac driver. After this last weekend I'd be confident taking turkeys out further, happy to try 150yards. And I think 100yards would be a good limit for broad side chest shots on goats, and 50yards for head shots.
Thats my 2cents for now.