It still is possible that you have some mechanical problems but without viewing a datalog it can be tough to point fingers....Despite what some people and companies will admit, custom tuning for each specific car can be beneficial....In polski's case I don't think the tune was solely to blame but there was an unwillingness from LMS to alter the tune. Although there were no mechanical problems to be found.
You may have a weak fuel pump but we are speculating without a datalog. You may have an ignition problem since you are mentioning misfires but again a datalog with specific PID's would help.
I will say from the logs of LMS tunes I have seen, the typically don't run enough boost to cause fuel pressure issues which is why it's easy for them to sell "set it and forget it" type tunes...They were developed and tested engineered tunes, so while I would not call it a custom tune for your car it is not your run of the mill "canned" tune either. And that's also why I wouldn't be quick to call your tune the problem...I've seen it too many times where a person's car is not mechanically ready for a tune but people do it anyway...If you have a problem before a tune then you will have a worse problem after the tune.
Good luck getting them to acknowledge any of your so called tune issues.
We have seen it here before whether it's from someone leaving LMS for a resolution or going to LMS for a resolution, unfortunately your end game may be to switch tunes if you are not happy. You may be asking for something that simply won't happen.