Does the car every drop from fast idle without disconnecting from the MAP? Is idle speed high on cold startup or does it do this on a warm engine?
First though, since it reacts when you disconnect it from the MAF, I'd suspect a bad MAP (I've gotten a few bads one even new in box) or the hose to the MAP is cracked or open or you have a vacuum leak somewhere.
Fast idle has only a few culprits - throttle stop setting and vacuum leaks, possible there is a vacuum leak that is hidden. You can try hitting the hoses with a water + a few drops of detergent mix and wet down the rubber hoses and unions as the car is running. If the idle drops suddenly when you spray a component, you'll probably found the culprit. Similarly, check around the throttle body and intake manifold. Could also be an issue with the IAC valve on the throttle body, clogged PCV hose/valve or a faulty coolant temperature sensor.
A vacuum leak in the engine (manifold leak, stuck open EGR valve, leaky PCV hose), may cause the MAP to read incorrectly, causing the ECM to use incorrect data. Timing that is off can also affect engine vacuum - good idea to check ignition timing to make sure it is on spec. Also a good idea to do a quick compression test. If vacuum fluctuates between cylinders - that could cause some of the headaches you see there. Worn valve guides, leaky piston rings, etc. - compression test will atleast see if anything is grossly worn out.