I like the sound of the second shop so that sounds like the way to go. But a few points......
The filling of any cylinder will result in expansion of the gas. This happens as the gas expands into the less full cylinder and is subsequently re-compressed as it fills. Simplistically.... as the air enters the cylinder it is doing the happy dance and the molecules are are less constrained. As the cylinder fills they get crowded together and friction, lack of freedom results in too much energy so it is released as heat. heat results in expansion and the air is in effect fluffed up. If you do a fast fill you can drive the volume of a given amount of air up to where it pressurizes as 10% more. A fast fill to 300 may easily be only 2700 when cool. This can be managed to some extent by:
* Slow fill
* Filling slow from cooled banks of air
* Bringing cool cylinder in to fill never hurts
* Filling with the cylinder in a water bath, whether you like it or not.
This is commonly attributed to Charles law but some consider Gay Lussac Law a better fit for the cylinder fill scenario.
Now the water bath does have a very limited effect I have come to believe and as such probably is not worth the risk of introducing water through sloppy technique. Remember that air is an insulator so once you have that hot ball of gas in there it's not in a big hurry to transfer energy to the cylinder walls. Air in direct contact will cool and there will be convection and very limited conduction across the gas mass. All told a cylinder needs about 4 hours to get from excited to steady state. I wait until the next morning to do a final check Y tag of my fills for this reason.
The shop that allows an hour for a top-off can come reasonably close if the initial fill was gentle. Better still if that add an extra 100- - 200 PSI above the working pressure. The only pressure that really matters is steady sate at 70F. A hotter cylinder should be at a higher pressure. it's no different than of you took a perfect fill at 70F and left it in the sun in a vehicle on a hot sunny day so don't worry about the cylinder.
Slow fills are your first line of defense, followed by a top-off. Better yet is dropping them off and coming back a day latter so the top-off can be done on a cool stable cylinder. If the shop has the cylinders waiting in the sun all bets are off!
I strongly suggest that you make sure to check each cylinder after it is off the whip. Do not just view the panel gauge. I have seen repeated human errors of party opened valves resulting in grossly short fills while the panel said things were at equilibrium and up to pressure. The time to discover this is as you accept the cylinders, not at home or at the next dive site. It also sends a message that you have expectations.
Pete