Is it possible to remove an app from the Play Store's "installed" list but keep it installed? I can't seem to find a workup on this.
That is possible, but requires a rooted device. Some apps provide a feature to accomplish that, e.g.:
Note that, even once achieved, Playstore refreshes those "links" – usually within ~24h. The first app takes care for that itself, and with Titanium you can setup a corresponding schedule to repeat the action (hint: use a filter, store the filter definition, and use that for the "scheduled task").