I never really got an answer, or I guess more accurately there wasn't an answer better than "it works the way it seems to work."
I set up a whitelist on eduapps center and use that to disable apps we have installed (that don't register as installed on the apps page), and that works pretty well - the issue is tool discovery, and how to inform faculty that disabled tools exist in the moment when they are trying to figure that out.
It would be great if the whitelist view could get a list of installed LTIs from an organization's instance and it would be possible to mark tools as "installed" and associate them with already installed LTIs in cases where they don't show up -- and also to make it slightly more clicky if someone tries to reinstall an existing app.
This might sound unnecessary except that here's what an instructor on our instance of Canvas sees in a new course when they navigate to Settings > Apps (in terms of installed apps):

Compare this to the actual list of apps that are actually installed at the root account level (and thus available to activate via Settings > Navigation or via assignments, etc. -- I bolded the ones that show up in the edu app center as installed:
Ares
Box
Campus Pack
Canvabadges
Cengage Learning MindLinks
Chat
Echo360
Ensemble Video
Examity
Google Apps
LibGuides
LTI Maps
Macmillan Learning
MH Connect
MyLab and Mastering
Office 365
Pearson Revel
PowerBi
Roll Call
SCORM Cloud
SCORM LTI
TED Ed
Turning Technologies Account Registration
Turnitin
Vimeo
VoiceThread
W. W. Norton.
WileyPLUS
YouTube
This is the disconnect that I'm trying to find an answer for - people go to "the app store" to add features, they don't check the navigation area, and in a few cases it causes support headaches because "ares is broken" or "the turnitin integration doesn't work" but what's really going on is that instructors don't realize/remember that the edu app store isn't a reliable indicator of what external apps are actually available.
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