The one rule
Every email in here obeys a single rule, and if you only take one thing from this document, take this:
Give them one specific thing to do, and one dignified way out.
That's it. That is the difference between an email that gets answered and an email that gets archived.
One specific thing to do. Not "let me know your thoughts". Not "when you get a chance". A dated, concrete action: pay this link by Friday, reply with a number, tell me which of these two you want. Vague asks feel polite. What they actually do is transfer the work of deciding what you want onto a person who has forty other emails, and that person will choose the one that requires no decision.
One dignified way out. People don't ignore you because they're hostile. They ignore you because replying means admitting something awkward — the budget's frozen, they forgot, they went with someone cheaper, they can't afford you any more. Silence is the cheapest way to avoid saying that out loud.
So say it for them. "If the budget's frozen, tell me and we'll work out a plan." "It's more than you wanted to spend — that's fine and it doesn't offend me." The moment the awkward thing is on the page in your handwriting, it stops being awkward, and you get a reply.
Every template here is that rule twice: an ask with a date on it, and an exit with no shame in it.
What this means for the tone question
You are probably worried about sounding aggressive. Look at what actually makes these emails land — none of it is force. It's specificity and an exit. You can be extremely warm and still be completely clear. What you cannot be is vague and expect an answer.
The word to delete, everywhere, forever, is "just". Every instance of it in an email is you apologising for having sent the email. Find it, delete it, send.