This is what i do.

I take at least my drivers door off before winching it in the trailer so I have access to the shifter. If you have glass doors why not. My Cuda has steel doors that were gutted and I always removed it as well. Easy enough to do to gain access. I think if you mostly tow locally it likely does not matter at all. However cross country stuff IMO putting it in park is a good idea. We also use chassis stabilizers on the dragster and all tube chassis cars. Shock take a beating towing as does the chassis. Dragster gets two bladders door car/truck gets one under 4 link crossmember.

are tie downs being used on the tires or the chassis ?
i have noticed lately that new cars are being transported with the tie downs looped through the wheels [when possible] or over the tires.
any opinions on these methods ?

If it's a standard passenger car, no big deal being strapped down at the wheels. I strap down at the chassis to avoid shock travel as much as possible (adjustable shocks).

Some years ago I read a suspension book that recommended blocking the chassis on frequently trailered vehicles. When you tie it down it moves with the trailer not independent of it and to keep from damaging tuned suspensions .And I suppose these were manual trans cars. Sounds like a PIA but it wouldn't matter if the car was in neutral.
BTW next time I'll try tie down then put in park!

I’m sure I’ll get called out as anecdotal, but, techs would momentarily engage park, to “fix”, stuck governor valves on A470’s.

Actually this was done way back before the 470. I’m interested in why you mention this here.

Because the pawls or the supports didn’t break. Did they get damaged, don’t know, but we didn’t stock either.

Understood now.

For clarification when throwing it in park at speed the pawl ratcheted off the support and simply vibrated the governor valve and weights and usually freed them up. Towing in park with a loose car had the vehicle weight loading and unloading the support putting all the load into the pawl pivot/housing.

Rail car was the worst - since the vehicles were not loaded on an angle like truck transport.