Changing my phone number, while keeping my old super cheap plan?

You should be able to keep your plan with the same price.

Because "Change this phone number" is not within "Adjust plan" menu.

you will lose your current number

Changing phone number does not change your plan.

https://fizz.ca/en/faq/how-do-i-get-a-new-phone-number

So you will keep the same plan and price that you already have.

However, if you want to port your number over from another provider, you will have to activate a new plan, at current pricing.