Can I extend my stay by simply walking across the US-Canadian border
and then walking back?
In principle, yes, that could work, assuming you have the necessary documents to enter Canada. There's no rule against doing that. You wouldn't be so much "extending your stay" but rather leaving the US and then seeking entry again on the Visa Waiver Program. Of course, whether they let you in or not is up to the immigration officer, and they might decide to take the fact that you have just been in the US for a long period as a negative factor in their determination.
And/or is there any simpler way to "switch" from J-1 to ESTA, without
leaving the US?
If your J-1 doesn't have the INA 212(e) 2-year home residency requirement, you can file I-539 (paying the $370 fee) for Change of Status inside the US to B2 visitor status. You can't (and there would be no point to) change to Visa Waiver Program status; B2 status gives all the rights of VWP and more. You wouldn't be entering the US so visas and ESTAs are not relevant. The application takes many months to process, but you are allowed to stay in the US while the application is pending, even if your J-1 status ends in the meantime.