I would never fork out that much to move that, and I think his estimate is accurate dealing with that cast iron and running a new bulkhead, then trying to get it to where it used to be below as well. Just open up what you can and leave a small wall for the mechanical. Either you have an unsightly large bulkhead, or a small wall. Looks like you would only need 3 of those stud bays. Plus removing that cast iron will result in more noise downstairs if they use PVC which they probably will. PVC makes more noise on horizontal runs. If you want to hear the toilet water moving in your kitchen then go for it. The current cast iron keeps noise very low. You could use that wall for cabinet and countertop space too.

Even with your detailed explanation & the pictures, I'm confused on what you are trying to do. Davidandkasie asked a very valid question. For a typical ranch home the area that you show a header going is typically a ceiling joist. I understood your response that the load above is "air & insulation" plus the ceiling itself but then the question is why do you need a header? To support what? What makes that a load bearing wall? It has to be there to support some kind of load. Now if the header is actually in the crawlspace (i.e. supporting the floor area) then the following applies. If you go strictly by the 2006 IRC Residential building code then the header spans for INTERIOR bearing walls are dependant upon the building width which for a ranch is typically the depth of the building (i.e. perpendicular to the roof ridge). For a 1-story ranch & 20', 28', & 36' building spans, 2-2X6s can span 4'6",3'11", & 3'6" respectively, 2-2X8s can span 5'9", 5'0", & 4'5" respectively, and 2-2X10s can span 7'0", 6'1", & 5'5" respectively.

Your picture seems to show 2x4s, a doubled sill plate, a gap, then a header. If that header spans from an exterior wall to an exterior wall, the 2x4s and doubled sill plate aren't doing any work other than holding up drywall.

With no living space above the only thing the wall can be "bearing" is the weight of the ceiling. Surely you've determined that the ceiling joists run perpendicular to the wall, right? If they run parallel it is not bearing in any way and can be completely removed if you like. If the ceiling joists run perpendicular then it's best if you get into the attic but there are some clues as to whether or not it holds up the ceiling. If the ceiling joists lap over the wall (they meet in pairs) it is certainly bearing. If not it all depends on the span and the size of joists. In general though nearly every such wall without joists lapping over it can be considered a partition wall. If it is a bearing wall one of the best ways to deal with it when only attic space and you're only bearing ceiling weight is by using an "overhead" header (it sits on top of the ceiling joists) to which you attach the ceiling joists with joist hangers. This allows you to completely remove the wall below. Of course you must have proper support at both ends of the "overhead" header.