"It's not like they'll simply 'email' me a counter - they'll want to know why I'm leaving, whether there's something they could do to try and keep me here, etc. There's a lot of discussion that they'd want to have before doing a counter offer, and the point of my question is that I want to find a non-rude way of asking them not to waste their time on that."
Here's a resignation letter for your situation,
"Dear team,
I'm hereby resigning from the position of [position] at [Company]. My final full day will be Wednesday July 3rd.
My plans and location from Thursday July 4th are settled.
Thanks for the great experience at [Company]. Please let me know every way I can ease the transition and ease any paperwork.
Cheers, F. Attie
That's all there is to it.
DON'T say anything explicit, such as "do not send me a counter offer" or "no discussion entered in to".
The closest you can get to being blunt is this language:
"My plans and location from Thursday July 4th are settled."
or perhaps
"My plans and location from Thursday July 4th are settled, thank you."
As my shrink says, "you can only be responsible for you".
If some person at the organization begins talking about the issue - that's not you, that's them.
It won't happen, but in that case just politely say "Ah. My new plans are completely settled from the 4th. Thanks."
Same by email, or spoken. The closest you can get to being direct is the phrase:
My plans and location from Thursday July 4th are settled.
Hope it helps!