You can actually do a regular FHA loan and have the major items corrected after the appraisal and final loan approval, but before the loan closes. The appraiser just has to come back out and make sure the items are complete. If you elect to go this route, it might also have some leverage to negotiate for the bank that owns the property to assist with the repairs - the furnace and water heater items are considered health and safety issues, which many banks will help with because they prohibit many, many buyers from buying the property.
That way, you don't have to add money to your loan, and you don't have to wait the extra time it takes to do a 203K. Of course, it does require that the bank that owns the place work with you on getting the repairs done. As good of a deal as it seems like you're getting, you should consider doing what you can to avoid losing the deal over a few repairs that itsounds like you'll need to make at some point very soon, in any event.
The 203k is not the worst thing in the world to deal with and depending on the contractor that you select there may be a lot of the things like gutter cleaning and power washing that you can do yourself. They may have to quote it in the bid but if you do the work they do not have to charge for it.