Alignment, with new tires vs used tires? Is there a difference? What, how much?

The only change I make to my set up with new tires...is to stiffen the rear sway bar approximately 3/8". This is to reduce the understeer. After about 4 or 5 heat cycles then you will need to soften the rear bar back.

Two questions. First, what is the reference point for the sway bar? Do you measure it by the end protruding from the collar? Second, has anyone ever used one of those Northern Tool or Harbor Freight tire changing stands to mount/dismount tires? Local tire shops charge a ton and don't seem to like changing my tires.

On the original poster's question, the only difference between old and new tires for alignment purposes is likely to be corner weights given that used tires may not be worn evenly side-to-side. I doubt that it would make any substantive difference.

On the reference point for sway bars, general rule is the measure to the end of the sway bar. Note that the actual stiffness can differ depending on which way the bracket is mounted since it's offset. We ended up reversing the fronts to get more stiffness. I can bind, however, at the extremes.

I'll leave it to others on the mounting/dismounting (and balancing) your own tires. Since the cost, at least for mounting, is covered in the Goodyear purchase, it's not that much of a cost to get it done at the track or the local dealer's shop (though swapping used tires front to rear can get expensive.)

When I had Shelby's I used Walmart occasionally as they were dirt cheap, but getting tires mounted on the right rim, in the right direction, was a challenge until my wife came up with some colored stickers that we'd put on the wheels and rims. Then we'd tell the changers to match the dots! Would not trust them with the Welds (had my first one destroyed at the track by the tire changer who made good on a replacement) or the new wheels.

I measure from the end of the sway bar to the face of the fitting. Moving the fitting away from the end stiffens the bar. I have some PCA friends that bought one from Northern to change their track/autox tires. They also bought a tire & wheel balancer. It seems to work for them. But I wouldn't do it.
I have found that using a "six pack" tire (2 fronts & 4 rears) rotation works really well. Starting with new tires, I swap the rears to get 4 or 5 heat cycles on each one. Then keep the total heat cycles approximately the same until all six are used up.

I use my HF tire tool and bubble balance about twice a year. Works fine but you'll work up a sweat!The tool must be secured to the ground and it can be rough on the wheels if your technique is not good.

Here in Houston I have good luck at my local Discount Tire store - they charge me $10 per tire to dismount and remount and balance - and their machine does well and they are careful with the wheels.