Yes, your hanger can be repaired. I done a few broken hangers on aluminum frames. I think Kline bikes are built with 7000 series alum. 7000 series can be allowed to air cool without any big loss of strength. You will have to remove the paint from the area, any paint sucked into the weld puddle will weaken the weld. I still don't know why any frame builder would build an aluminum frame without a replaceable hanger. Its not a huge job, should only take an hour or so. (hard to say without seeing it) Most weld shops would charge $50 or so, some more some less. You will need to strip down the frame. And after repairing the hanger you may need to realign the hanger.
There may be another way... Take a look at www.exposales.net
they sell an aluminum brazing rod. It melts at 735* and flows into the gain of the base metal (alum melts around 1100*) A propane torch would work well. The rod is called HTS-735. I have not used it myself, but I have seen a few things repaired with it. I would not use this to repair a high stress aera such as a cracked headtube, but it should work on a hanger. the rod has a tensile rating of 45,000 psi and shear of 31,000 psi.
"When the spirits are low, when the day appears dark, when work becomes monotonous, when hope hardly seems worth having, just mount a bicycle and go out for a spin down the road, without thought on anything but the ride you are taking." - Arthur Conan Doyle