There's no feasible way to "let" a virus spread faster than another. Some spread faster than others naturally, and some mitigation tactics (c.f. masks vs. gloves vs. hand washing vs. social isolation) work differently against different viruses. But there's no way to pick a specific strain and say "we want everyone to get that one".

Now, you might culture it in a lab and then inject it into people deliberately so they develop antibodies that then work against the "true" virus. This technique is called "vaccination".

This is a report on some progress on one particular vaccine type. But it's minor progress. What we need is an attenuated strain. What this shows is just that there are some spreading strains with gene deletions (which is the kind of mutation which tends to produce attenuated strains). There's a lot of work to get from there to a vaccine.

>There's no feasible way to "let" a virus spread faster than another.

You can certainly "let" a virus spread faster than another. Society chooses to let the flu spread more easily than ebola despite them having similar R0.

In this case, you could vary school closure criteria, tracing effort, or quarantine duration by strain.

Sure you could, via intentional infection by cultivated strains.