Civihosting responded privately to my post in the main group about issues with some punctuation or other characters in page names and media filenames and that stimulated some interaction with my Dokuwiki trial out of which I've learned some useful things. I must give Civihosting credit for going through multiple re-migrations over the weekend as they tackled one problem after another. Are we there yet? Too soon for me to say as my time to inspect is limited and I want to record these other lessons I've learned on the user side that I have been exploring in parallel with their revisions to their migration tools.
Dokuwiki has optional plugins
Batch Editing with BatchEdit
I wanted to fix the broken links to images stored on postimages.org servers as reported. Can't do it in bulk on Wikispaces, can be done with Notepad++ on the exported files but they had already been imported into Civihosting's Dokuwiki. The default configuration has no global search & replace tool but Support suggested I look at BatchEdit. Alternatively, I could FTP download the pages (they are .txt files) and batch edit locally with Notepad++ and upload the revised files; however, that method would not record the changes in page histories.
The plugin does not scan file system for pages like grep or Notepad++ do. Instead it uses DW page index, so it can find only those pages that DW search can find. It also takes into account DW ACL to ensure that users can modify only the pages they allowed to edit.
With a little more research, I learned that Dokuwiki builds its full text search index incrementally as users access pages, not all at once. As Civihosting had just done a fresh migration, only 2 of the 15 pages had been touched by anyone.
Batch Indexing with SearchIndex Manager
To the rescue, I found the SearchIndex Manager plugin. Launching it, you see a progress report of what page number it is working on out of the total to be indexed. It's not blazingly fast which makes me wonder if it is basically browsing each page in turn to trigger the indexer, not actually controlling the indexer directly. Perhaps there is a more direct way for those knowledgeable in the workings of Dokuwiki and PHP.