BTW, I have found the .xml and .json files linked to the search function. Changing relevant http entries to https seems to work but this is tiresome, these modifications might get replaced and I'm not sure if everything is implemented correctly(eg. search suggestions).

If you copy the modified xml files to a searchplugins folder in the Firefox Profile Folder then those changes should be permanent as long as you use that profile.
You need to change the name of the search engine in the file to avoid Firefox rejecting a duplicate search engine.

See also:

• http://kb.mozillazine.org/keyword.URL
• http://kb.mozillazine.org/Location_Bar_search