I put together a small DEVONthink script that publishes the Markdown notes you have selected to Marked Share. The notes stay private, and publishing one again updates the same document instead of making a second copy.
Download
What it does
Select one or more Markdown notes, then choose Publish to Marked Share from DEVONthink’s script menu or the contextual menu. Text records named .md or .markdown count too. Everything else in the selection is skipped.
The first run opens Connect an app in your browser. Sign in there. The script never asks for your Marked Share password. The keys come back to a helper in your Applications folder and land in the Keychain. Hold Shift the next time you run it if you need to connect again.
One dialog asks for a folder. Leave it blank and new notes go to the library root. Type a folder that already exists and the notes are filed there. The share links are copied to the clipboard, and each record keeps the link in custom metadata so the record’s own URL stays put.
Installing
Open the package. It installs for the current user and does not ask for an administrator password. It adds the script to DEVONthink’s menus and drops the login helper in ~/Applications. The first time it runs, allow it to control DEVONthink when macOS asks.
More details
Folder rules, republishing, and the bits that will not survive the trip to the web (local images, DEVONthink item links) are written up on the project page: DEVONthink Publish to Marked Share.