Like Chevy said converting to MIG is about the only real option but some people do this successfully with flux core, it takes quite a bit of experience and even then it does not produce the best weld. On 22 gauge it could be a real problem
If you can possibly convert to MIG I guarantee you will not be sorry as the difference is nothing short of amazing. If you do convert then use the .023 solid wire until you get the hang of it then switch to Twenty Gauge and I think you will find you can weld better than you thought. Doing this conversion is not at all hard nor is it all that expensive to do with that little Lincoln which BTW is a good machine.