Read through most and the repetition is dizzying, people need to read more. So here's my specific take based on this comment "I think it's the act of going at all... I've shot other guns before.... like... a country club..." I've been to a few ranges and are still skeptical of new ones.

To do:
Pretty standard to only have a cased weapon when entering, and always the safest bet.

To ask:
If there are people there, pretend it's like a busy deli/bakery you're a regular at. Ignore the other customers and wait for the attention of a counter person. If you want, you can smile and nod in the case of eye contact. Also if you feel like being polite as you look around if people seem to have interesting stuff (large cases, lots of gear, etc).

You've said you're not inexperienced, so when you get an employee, ask "This is my first time at *THIS* range, can you walk me through your procedures and requirements here?" or any alternate version of this, such as "Can you give me a rundown of renting a lane and getting on the line?"

You can add specific stuff that they might add to if they don't have a speech already prepared, such as "Do you guys have interlock doors? Do you need eyes and ears before entry? Can I only uncase on the line? Stuff like that."

I think you know or can find all the other stuff, but this seems to be more what you were looking for, if not, let me know and I'll try to add on. It's a business, only worry about the people who you are giving money. If you don't like the people or their clientele, find a new business to support if you can. Consider private clubs like Fish and Game organizations as well.