You need a FLAT substrate for any new flooring material, no matter how you intend on installing it. The shingle thing for solid hardwood works fine. I have nailed through self leveling underlayment with no problems, however I had to resort to hand nailing with hardened spiral flooring nails, as my pneumatic nailer would not do the job. Floating a wood floor is OK...but the substrate needs to be FLAT there also. I hate the concept of floating floors and find walking on them to be a little 'creepy'...just personal bias.

When you lay the hardwood planks in place, they will be secured to each other using a grove and lock system and sometimes with glue. But you will also secure the flooring to a structure under the floor with nails to assure that the flooring is secure and firm. Generally this calls for laying a structure of plywood sub flooring that will provide the base to which your hardwood floors are attached. Here is a link that might be useful: F.A.Q. About Installing a Hardwood Floor

Do some excavation to see what is actually under the top layer--you may find several layers of flooring such as vinyl, linoleum, plywood or even hardwood if you are lucky. Once you get to the last layer, you may find your floors level. It is odd that the only subfloor is in that room--mine don't have any at all, just the very thick tongue-and groove flooring itself laid directly on the joists. I need to do my own excavating in the kitchen--I know there are vinyl tiles (mine), 70s sheet vinyl (there when I moved in) and under that, who knows? From the basement I can see the same t and g boards as in the rest of the downstairs, so I'm hoping it is oak to match the rest of the first floor. My ideal find would be original linoleum in a nice pattern I could use! Whether you could install new flooring as you suggest depends on your joist spacing, the thickness of the flooring, and the weight of your cabinets and appliances. When I moved in, my kitchen had a stove in front of the chimney breast, a refrigerator blocking the only window, and 70s plywoodish cabinets along that wall and forming an ell on the neighboring wall. There was no sag or deflection of the floor. My kitchen is about 12x12, so the span isn't too great, and there is bridging between my joists as in most 1900s houses. I redid my cabinets to cover the wall to the right of the window (found the original doors in the garage and built my own boxes), moved the fridge to the pantry, and replaced the stove with a newer one of the same size in the same spot. Yes, I should have done the floor research at that time, but I just wanted the 70s crap gone. :) That sheet vinyl was under the cabinets, so it was put in before they put the cheap ones in--but it wasn't close to original to the house. If you opt for huge fridges and restaurant size stoves, you may have a problem--but my appliances are standard sizes since I'm just an average person and not a professional chef wannabe. Food tastes just as good done on normal appliances--it is all in the ingredients, not the utensils.

I would cut out that section of subfloor and dig into the wall to investigate. Its possible the house wrap failed or you have a flaw in the outside sheathing. of course it could be something else entirely. but 13-18% is way too high. 8% is ok. You can leave the 1/2" if you want, but it tends to be bouncey, if adding another layer of plywood wouldn't effect anything else in the room, i.e. cabinets, then id consider it to stiffen up the subfloor. Also now that the subfloor is exposed, screw off the entire room. take the time to do preventative maintenance to avoid premature squeaks. and lastly...Good luck!