Suggestion: Measure just how much power the welder is really using (more-or-less)
Power meters aren't mysterious black boxes, just write down the meter reading before and after a welding project and see how many KWH were used.
Granted you still have the "background" use of the rest of the house, but as you noted it's all CF lights and gas stove/dryer so the background use should be fairly constant.
If you want to eliminate it just down the times you took the readings as well and take another set of reading immediately after the welding project over the same duration and subtract that reading from the first. You should get something reasonably close to the true KWH used by the welding.
Pete C.