If your tablet is android or IOS, it would be possible to write an app to do that.
btw the most efficient way to operate is to have the ESP simply output data as a json, and web page (or an application) is on the tablet.
No you can't access a new AP from the HTML or its JS code. ...
and from the original question:
... switch the tablet WiFi over to the ESP WiFi, open the downloaded webpage and have it initiate communication with the ESP8266 on the usual 192.168.4.1. ...
@kenn ... guess you should read the question before answering ...
and yes, you can copy your HTML and JS files to an Android device
open them with Chrome (file:///sdcard/... or wherever they are...)
and have them redirecting queries to an external device...
it's called CORS, "Cross-origin resource sharing", not "massive security hole"
you will have to properly take are of it in your code
just saying...
Or is there something inside your ESPBOT code as well which I can't locate ?