I would say look at and contemplate muskieratboi's post. While I am not sure of the merits of all this (it is twitter so nothing interesting happens there) I can happily write it off as "to each their own" and muskieratboi's post presents the easiest way for this to happen. Someone might well be able to one day either provide a nice patch/plugin to do it, or remove/alter the relevant parts of the existing setup to do it but that would take a fair bit of effort and you will probably have to do it yourself (it is a very niche thing to want and there are far bigger problems to tackle).
Anyway
If the resulting images appear in a place on the file system, one we can access during a game and fire over FTP or something (I believe we have always on FTP these days), you could have something on a PC/raspberry pi/phone/whatever connect to it every so often, check for new files, copy them off and post (either automatically or throw a message to something else to confirm) and there you have it. We have loads of scripts to do similar things for any number of other devices (typically cameras and data logging devices) and if you have the always on FTP part on your switch the rest is probably something a simple guide already exists for (a casual search just now for twitter bot image posting yielded several with scheduling and whatever abilities).
There are doubtless setups this might not be ideal for but I imagine most of the time you would care to tweet such an image you will be in range of a known network you control, and if not you might be able to do something like a hotspot on your phone/tablet.
