Torbjorn,
Is it possible to clean the injector yourself?
Yes, if you feel competent enough. you have to be aware that any scratching, scuffing or inclusion of foreign material will render the unit useless. If you are not confident, then put it out to a specialist.
Basically the fit is metal to metal and no lapping is allowed if you make a mistake. Cleaning must be scrupulous and orifices must not be marked or scratched in any way. Rebuild under clean fuel is the order of the day. Apart from that, no problem.
They also need setting to pressure which is done using a 'pop' tester. If you don't have one send it to the specialist. Got the idea? Put the job out rather than risk messing it up. Cheaper. Especially if you don't have a working spare.
You could rig up a compressed air supply to the injector hole. That way you will know where the gas is leaking. Done all the time on old iron. Good in cojunction with, or as an alternative to, a compression test.
You may even have a valve which is not quite closing properly, or the engine may have been left with one valve open and that may be giving trouble, due to corrosion.
Regards, RAB