That is a really strange setup. The breaker in the main that feeds the garage subpanel is 50A. So then why is the subpanel's main cutoff a 60A? I didn't think that would be allowed, but I'm not sure of a code reference for that.
So with the subpanel really being 50A, and it having other circuits in it, you shouldn't do the whole 50A for the car charging circuit. I would probably say a 30A, like a 14-30 outlet. Really, don't be so dismissive of a 24A charging rate. But 40A might be OK too. From the chart
@mrau posted, the Model 3 gets about 22 miles per hour recharged. (Y should be similar--maybe 21?) So in 8 hours overnight, you would get about 168 miles refilled. That's pretty solid.