I have experience welding 6061 AL to 304.  It is a tough task to say the least.  Like mixing oil and water.

There are really only two welding processes that might work:  friction welding, and explosion bonding.  With both of them, you really end up with what resembles a diffusion bond with no visible fusion zone on a metallography view.  The welds are also brittle.

We had to withstand thermal stress of about 400-500F.  The thermal expansion stress differences were enough that we had massive problems with cracking the brittle welds in service.  (We needed a hermetic seal for a jet engine part).

Our yields were as low as 25% with friction welding.  We switched to explosion bonding and got yields up to 85%.

We did not try brazing.  Some people have tried brazing al to ss.  There are problems with brittle intermetalliac compounds with brazing even.  Also, they say plating is reqired. I think they use a tantalum or titanium interlayer.

Good luck!