Thanks for sharing this!! This looks like something worth sharing with our professional support team by emailing support@rstudio.com so we can track more formally!
In any case, rest assured that you do not have too much content (we have demo servers with several thousand deployed content endpoints, for instance, and they do not present this problem).
Ultimately, this looks like a lock conflict on the SQLite database, for some reason.
When you post a support ticket, can you share your /var/log/rstudio-connect.log file? Also, if you can share a bit more about your architecture, that would be helpful. I presume you are using the SQLite database?
Another idea, would it be possible to share the output of:
lsof /path/to/my/database.db
# by default /var/lib/rstudio-connect/db/connect.db (I think)
Thanks!