8640 is still a .40 carbon material. A preheat of 350 F is a little on the light side. 400-500 F would be much better. More if restrained.
The big thing is to be sure the entire weldment is very close to this temp. "Soaking" the weldment in the proper preheat is important. You are trying to be sure that the entire weldment is near the same preheat temp. Hard with a torch, much easier with an oven or insulation.

The weld does not have to "beat the plate". 7018 or an E71T-1 fluxcore wire should work well, as long as preheat and interpass temp limits are observed. An interpass of +/- 50 to 75 degrees F should be maintained, if possible. Wrapping in some type of insulation will slow the cooling rate, and therefore reduce hardness to a great extent.

Whether the weldment is to be heat treated is another concern. If so, the above procedure is useful. If not, preheat to about 300 F and weld with 312 stainless. While 312 will not respond to heat treatment, it is extremely strong, ductile and crack resistant. Cooling rate usually has very little, if any hardening effect using 312.

Hope this helps some...

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Good Luck
brande