I would argue that if the customer wants to limit you to less productive processes, then limit it to less productive processes. But tell him he is going to have to pay for it. This is an old problem. The customer, not trying to be too unkind here, is trying to give you a toolin. They want something extra-in their mind-on the cheap. These alloys are welded by the ton every single day using these processes, and SAW to boot.
Heat input control is heat input control, regardless of the process.
Also, since this is a dissimilar to carbon steel I wouldn't worry about getting too sophisticated with filler alloys. The 309Mo as Avesta recommends will be fine. If the 309 won't handle the service the carbon steel BM won't either.