In that <1 second, the OH can react with methane or CO. The more CO in the atmosphere, the more likely it will find the OH before the methane.
It is like throwing breadcrumbs to ducks and geese. The more ducks in the pond, the less crumbs the geese will get.
Methane levels don't impact OH levels (it is always consumed immediately). OH generation levels can impact methane levels. CO levels can compete with methane for OH as is it generated.
You are correct that OH radicals regenerate, but more methane => "breakdown capacity" becomes overwhelmed.
This is known as zeroth order kinetics, similar to alcohol metabolism. Drinking 2 beers = 3 hours until sobriety; 4 beers = 6 hours. Your liver has a fixed capacity, so drinking twice as much doesn't double the metabolic rate.
I'll add that you're also entirely correct: if there's some long lived chemical that catalyzes OH formation, sending that up instead might be a good remedy IMO. If there's no collateral toxicity...
> So, why not produce a bunch of OH? Because OH has a half life of less than a second. Hmm.
These two statements seem to contradict? If the chemokinetics of OH generation is less than a second, then how can it be used up in the atmosphere?
Assuming the <1 second kinetic is correct, there must be a dynamic equilibrium producing it in the atmosphere to begin with. In such a case OH is not truly being used up in any real sense. It's whatever that generates OH is being used up, and that can be artificially boosted.