I understand your pain.
With regard to the dealer that insists the problem is you ... have these people actually shown you themselves that FMQ can be done on YOUR machine, or are they just telling you that it can be? If they have not shown you, I would start there and tell them that if they can do it properly while you watch you'll believe that you are the culprit.
With regard to you ... have you been able to FMQ successfully on a different machine? If not, you need to try. Wheter it is a friends machine, or a machine at a dealer (bring your own sandwich to quilt), you need to try it to make sure that YOU can do it. Since your clearly not experienced at it for lack of a good machine that allows you to practice a lot - don't expect it to be perfect, but you should be able to do it to some extent.
IF the dealer cannot duplicate FMQ on YOUR machine, and IF YOU can duplicate FMQ on another machine - then yes, the new machine might just be the ticket.
I honestly don't understand your dealers statement that you might not be able to have much time on the machine, that's pretty weird and counteproductive to selling a machine. So what I would do is take all the time you can on the machine, even it's in multiple sessions, then if you decide you like it - order it from the other dealer (who I'm sure will be happy to stock it if he knows he has a sale!!). Again, don't discount used machines either.
But before I laid out money I would be sure that the machine is what I needed. So you need an experienced quilter to try your machine, and you need to try others. Perhaps there is a guild or an LQS that hosts sew-ins and you can try other machines.
Good luck.