Which process are you using?

There is no way to eliminate or reduce this shrinking and distortion, it must be considered as part of the design, fit-up, and welding processes. The only alternatives may be to look into a mechanical connection such as Victaulic or other mechanical clamping systems.

Shmally,
sounds like Sch. 10 SS. It very much depends on what the configuration is you are welding and what welding process. Lets take GTAW as an example. Welding a 16" header with multiple weld-O-lets on it is one issue. Welding fittings on to straight runs of pipe or pipe to pipe welds is another. The latter example can be easily controlled with good fitters and exp. Sch. 10 welders. Quartering the weld joints is one way, which is the process of applying equal application of heat input. You basically weld a quarter and then weld the opposite quarter.  Understanding the distortion direction and welding accordingly to control distortion. But the joint has to be plumb, level, and Square to start. That's where a good fitter comes in. We do a lot of Sch. 10 S.S of all diameters, and have to apply these practices every time.

Heat Sinks.
On flat stock SS I have TIG Welded 3-6" than water quench.
Good Luck your just over 3/16" thk on a large diameter.
Not sure if these are options...