Monster 800 misses when hot

[ccasazza]

So against my better judgement, i picked up a 2004 Monster 800 with 1800 original miles.  The bike has been off the road since 2012 but was reportedly "serviced" about a year ago.  The timing belts look like new. 
The bike will start up immediately and idle.  It runs well for about a mile or so until it warms up. Then it starts to misfire and loses power and sometimes stalls. I thought it felt like a fuel problem but that is just a guess.  I replaced the in tank rubber fuel likes since i had them left over from my old ST2.  That didnt help.  I really dont want to start guessing and randomly replacing parts so i am looking for any assistance that the more knowledgeable ones here can share.  If anyone can point me in the right direction or 2 to start, it would be greatly appreciated. My next guess would be either the fuel pump or tps.  Am i on the right track?
Its a tough problem to diagnose because it has to be a hot motor and by the time i get it home and onto my lift, it cools down and runs normal.
I am really a Ducati beginner but have been working on bikes for years. Is a diagnostic tool for the FI system a must have?  I previously had a first gen M900 and an ST2 and a 750S but they were pretty trouble free.
Any help would be greatly appreciated.

[Howie]

A scan tool would make life a lot easier.  Is it a random misfire or a cylinder dropping out? 

[ccasazza]

A scan tool would make life a lot easier.  Is it a random misfire or a cylinder dropping out? 

It almost feels like the bike is running out of gas. The bike bucks and wants to stall.   It goes away most of the time if i get off the throttle and gets worse with more throttle.
Is there a scan tool that works ok and wont break the bank.
Thanks

[Howie]

Assuming you changed the fuel filter when you changed the fuel lines and the gasoline is fresh, first thing I would look at is fuel venting.  Easy check; when the bike starts running poorly, pull to the side of the road, open cap and see if the problem goes away.

As far as aftermarket scan tools go, I don't know what is presently available.  TechnoResearch only does Harley now.  One thing I learned is sometimes it is worth it to go to a good shop.