Are you really familiar with guitar setup and repair? If not it might be best to take the guitar to a luthier.
Breaking down the information you have provided:
You say "the issue is with intonation" and you also say "I cannot move the string shorter...". Shortening string length would result in lower tension not higher tension. You should not be adjusting string tension by changing bridge intonation. Bridge intonation is used to fine tune the scale length to improve the tuning across the length of the fretboard.
It is unclear what other adjustments you have made. Was bridge height adjusted? Was the tremolo spring tension adjusted? Did you make truss rod adjustments?
The breaking of the E string could be an indication that you have a burr or some other blemish on your saddle or nut. Also, when you say you pulled up, how far did you pull up?
An increase in tension of the strings could be the result of a backbow, an improperly setup tremolo, and/or shifting of the tremolo mounting studs. Are any of your frets loose or lifted?
Is the neck tightly and securely attached to the body?
Have you removed your tremolo cavity cover? Is there anything that got into he tremolo cavity that could be interfering with the operation of the bridge?
Are your tuning machines loose?
Is the nut securely attached?
Is there any damage to the headstock, neck, body, or neck pocket?
The tuning instability could be the result of an improperly set up tremolo, loose tremolo mounting studs, saddles that are not locked down.
It is not 100% that the string breakage is tied to the tuning stability issues.
The string breakage could be as simple as your saddle could have gotten sand or grit on it and gotten scratched during the move. Or it could have developed some rusting.
For the tuning stability I would first make 100% sure that the tremolo is set up properly with the bridge floating level when the guitar is in tune. Pay attention to the sustain block, it should be parallel to the sides of the tremolo cavity when level. Once the bridge is level measure the relief on the neck. If you do not know how to measure relief take the guitar to a luthier. You should not be adjusting your truss rod for any purpose other than to set relief. THE TRUSS ROD IS USED TO SET RELIEF NOT ACTION!. Once the tremolo is floating level and the relief is properly set, if the strings are too high or low you can adjust bridge height to set the action. The action should be set by measurement, not eye.
To assess the saddle, visually inspect the saddle. Do you see any scratches, burrs, rust, or debris in the area where the string touches the saddle? Run your finger nail over the area where the string touches the saddle. Is it smooth?
As for dumping the guitar on Reverb. I think this is a really bad idea. If you accurately describe the condition of the guitar, you will have to set the condition as "not functional", disclose all of the issues with the guitar, and sell the instrument as a parts guitar. You will not get much money if you do that. If you use any other condition to describe the guitar and fail to disclose the issues, you will likely have a return for "condition not as described" and a bad review on your Reverb account. This would only add to your frustrations.
My advice: take the guitar to a real luthier. A good luthier will be able to tell you what is going on and should be able to fix the instrument.
