Keeping old clients working after rewriteBase change?

Nextcloud version: 15.0.7
Operating system and version: Debian stretch (Apache & PHP 7)

Hello. I upgraded from ownCloud to Nextcloud long time ago, but kept the https://foo/owncloud/ URL. Mostly for esthetic reasons, I have now moved the installation to https://foo/nextcloud/ and everything is working… except all the configured clients that are still configured to the old URL. We are using a mix of DAVdroid, iPhone CalDav/CardDav clients, Mac/Linux owncloud/nextcloud desktop client, Android & iOS Nextcloud & ownCloud apps, and maybe others.

My question is: How can I configure things so the clients continue to work with the old URL?

I have tried this Apache mod_rewrite config:

    RewriteRule ^/owncloud(.*) /nextcloud$1 [QSA,R=301,L]

It works fine for DAVdroid, but the Linux owncloud desktop app says ‘No connection to server’.

Do I need to setup a proxy? How should it be configured?