You are making excellent progress and thinking ahead.
Girls that age will mess with him (feed/brush/etc.) and have him accepting people in his world and his pen very quickly. Your girls will quickly become very trusting of him. Their safety depends, as I'm sure you know, on YOUR judgment about how close they can be allowed to get to him, and under what conditions. There is a reason that petting zoos do not have large adult billy goats in them for the human kids to pet....they weigh too much and at unpredictable times they decide to assert/test their dominance
I applaud your idea of making a chute from strong materials..the pallets...this should work fine....
The good news is that ultimately the horns will be removed....bad news is that when this happens you will lose your "handles" on the goat. Thus, I recommend you get a small halter from the feed store that fits him...strong, not a flimsy one but made of nylon or other tough weather resistant material. You can get him familiar, over time, with being haltered when being fed. Might even leave the halter on him at times so you will be able to have something to grab on occasion. Specifically, I'd leave the halter on while the horns are banded and until fully healed. Feeding alfalfa is laudable, but not required... you can use a less expensive feed and he'll still be very healthy and like it just a well.
The collar is a good start, but will be ineffective in properly controlling the animal. The halter should have a ring so a lead rope can be snapped to it and buckle type adjustments so it can be snugged to the head.
I looked at the photo of the animal... if this is your place, the fence you have is IDEAL and can be used for one side of the squeeze if the configuration works out that way. Make sure the sides of the squeeze are at least 50% taller than the goat is..... amazing how well an unconstrained goat can climb out of stuff. If you do get a halter, you can have a bar at ground level you can run the lead under, wrap around, and hold the head toward the ground...key to controlling the entire goat's body.
Screw worm medicine...haven't heard that phrase in many years...I have experience from the early 50's when there were actual screw worms and they plagued ALL animal husbandry folks in Texas. Thankfully, they have been eradicated from the USA now...but still you DO want to control the flies on the goat's head after the horns fall off. Else, you will get maggots where you really don't want them to be.
Best wishes...and let us know how it goes