Hi PaulZ!
Have you looked into the possibilty of using a laser welding system for your application, Electron Beam welding - maybe not? Just a thought... How about a micro-plasma arc welding??? Back in the day, Thermal Dynamics had a decent low current, (with a pulse/spot timer having settings down to about .1 sec or so) plasma arc system just for that sort of application and so did Jetline Engineering, if I remember correctly??? Besides, with plasma arc welding, you could significantly lower your heat input and at the same time, have more control of the weld size and depth of penetration... but since you did'nt post enough essential variables, I can only speculate and I do'nt like practicing blindly...
Come to think of it, Perkin Elmer has been using the above mentioned processes for very thin joining applications for quite a long time now:
http://fluidsciences.perkinelmer.com/default.aspx
It ca'nt hurt to contact them to see if they can help...
Another site that will show you some options in process selection for your application would be:
http://www.ewi.org/microjoining/microtech.asp#microres
I like what I see in Pro-fusion's website and I think that Micro-plasma is the way to go for you!!! GOOD luck!!!
Respectfully,
SSBN727 Run Silent... Run deep!!!