On the lookup tool for a user, add a section to move purchase and installs from one user account to another. At this page: https://marketplace.allizom.org/lookup/user/[SOME USER ID]/summary add in a "Move purchase and installs" option that takes a users id. Hitting merge takes you to a "Are you sure you really want to do this?" page with all the gory details. Or maybe a popup, whatever. Selecting yes actually does it, triggering the API in bug 1030461.

Not a issue for this bug exactly, but under what circumstances would this button actually be used?

The primary use case is for Firefox Accounts, users will have to register again with a new Firefox Account. In that case, if they don't use the same email, they might have no access to old purchases or installs. See https://wiki.mozilla.org/Marketplace/FirefoxAccounts#Migration

Is this something we will be promoting as a facility we can offer for the user, or just in case we get support emails?

There isn't the time for this, so being realistic, I'm closing it.