Well if it was jetted before and the standard Mikuni jets don't work I would wager there was a Dynojet kit in there. Do you have any pics of the emulsion tube with the broken bit in there? You may be able to gently drill out the broken bit and then screw in the old jet to repair the threads. It's brass so it's soft BE VERY CAREFUL!! What might be better is to get the smallest drill bit you can and drill a small hole in the broken piece of thread and then you have a hole in which to create a way to unscrew the broken bit.
For example if there is a small hole there and you have a tapered prescision screwdriver you can tap it in the hole gently untill it bites into the broken material creating basically a flat head then you can unscrew it. I think you can fix it but remember if something doesn't go in smoothly, STOP!! Especially on soft brass fine parts from carburateur's. If you want to keep Ivan's kit you will have to replace all the emulsion tubes($22X4) and replace the broken jet($5) if it's not broken too much, with only the last little bit broken it may have enough threads to screw in no problem.
If the bike was already jetted with a Dynojet kit what was the reason putting in an Ivan's? Was it this #2 cylinder misfire problem you posted? If we can get your bike back to at least running we may be able to help you make it work probably with the Dynojet. You'll have to make a descision either way to keep the Dynojet or Ivan's. Ivan's will cost you $100 but it's a great kit. If you don't want the downtime, put the Dynojet kit badck in there and we'll help you fix it. You didn't drill the airbox a la Ivan's instructions did you?
Because the brass is so soft you may be able to get a tapered drill bit and GENTLY drill away the broken bit in the emulsion tube untill its gone. Just be carefull these carb parts are easy to kill. Use low speed on a drill.
Can you contact the original owner about what was put in there? What jets did Ivan send you?
Also try and keep all the problems in one post so we're not running around trying to find how to help you.
This is probably easier to fix than you think. If you want to keep the Dynojet you could sell your Ivan's here no problem. If you had a second Gen Ivan's kit I would have bought it. If the emulsion tube gets totally phucked trying to take out the broken bit you might as well just order the stock tubes and install the Ivan's kit.