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It looks like you have a interesting alloy there. I have never dealt with this one specifically, but I hope this helps. UNS S30600 looks like it corresponds with ASTM/ASME A/SA182 F46. (18 Cr, 15Ni, 4Si). I have never heard of "intense water cooling when welding" before. Possibly you could tell us what they mean by that a little more. As far as solution annealing though, when it was manufactured, per A/SA182, F46 material is solution annealed at 2010F to 2140F and liquid quenched to below 500F. Since this alloy wouldn't be forming martensite, it doesn't need a temper following a liquid quench. I'm sure you would want to perform the same heat treatment after welding. Unless you are planning on heat treating yourself, a reputable heat treater should know how long to hold at temperature based on the thickness of the piece being heat treated, and the performance of his ovens, etc. I don't think you could do a localized heat treatment because even though it would improve the corrosion resistance and mechinical properties of the weld, other areas would be adversely affected that happened to fall into the temperature zones that the post weld heat treat was trying to fix.
I am a bit perplexed about the heat input though. Per ASME, if a weldment is solution annealed after welding, heat input (and interpass temperature) are not essential variables, even for base material with impact requirements. This is because, no matter what detrimental microstructures or precipitates are formed during welding, they all dissolve and the microstructure is reformed at the solutioning temperature. Since this is the case, what does it matter if you have high heat input and form lots of bad things in your weld/HAZ, or low heat input and form just a few bad things in your weld/HAZ since they will all dissapear with PWHT anyway?