According to the Lerner Symmetry Theorem, which has held up pretty well for decades except for a few edge cases, shows that export taxes and import duties counterintuitively have the exact same result. So Canada introducing export taxes would be like Canada simply reciprocating with countervailing duties, which just makes everything more broken.

My thought experiment is a bit different: what if Canada were to apply a fairly low across-the-board import duty on all US goods and services, probably at a low enough rate like 3% that it wouldn't be a big deal politically. And use the funds thus raised to fund varying export *subsidies*, product by product and rate by rate, on all goods and services exports to the US which are subject to US duties, designed to exactly match the US import duty rates on those goods and therefore nullifying their effect on end consumer prices. Every time the US duty rate on Canadian-made left-handed widgets goes up, Canada adds a matching increase to the export subsidy for them, and a really tiny fractional increase in the across-the-board import tax rate on US goods and services.

Results?
For Canada, it is by construction revenue neutral for the government, and no Canadian producers get volume hits from US tariffs.
For Canadian consumers, prices on imported US goods and services go up a small amount, but probably not enough to change many purchase decisions.
For US consumers, prices don't have any reason to change, since the Canadian export subsidy and US import duty exactly balance, so they can buy whatever they like from wherever they like, same as always, same old price.
The US government gets to have whatever tariffs they want on whatever goods they choose, and gets to keep the revenue from them, but it doesn't affect US consumer behaviour.

The cost to the US is a fall in the volume of US goods sold to Canada at the margin, due to the increased prices as Canadian retailers pass on the across-the-board Canadian import duty, but it would be small due to the low overall flat duty rate, and would not distort either country's economy as it's applied equally to all goods and services. Probably not a larger effect than the amount that currencies swing in any random year.

Jim