First of all, take care of the A.I.R. check valve first, or you will probably end up cleaning out the emuslion tubes again. You can plug it or cap it off until you get around to picking up the new part. Also if you are getting exhaust into the air cleaner, the vacuum switching valves on top of the A.I.R. check valves are probably bad also. They can be tested with a hand held vacuum pump.
Next, there is more than one adjustment to a choke. The spring tension is probably the most least likely to fail, and the most adjusted part of the system. The choke pull-off, or vacuum brake, is probably the cause of your problem. When you hit the throttle the first time, when cold, it sets both the choke plate totally closed, and brings your throttle up on high idle. The moment you start the motor, your choke brake, or pull-off, uses engine vacuum to open the choke plate to a specified clearance. It does this to prevent flooding. This adjustmint is very critical, and is also matched to the choke idle speed adjustment. This adjustment is done by bending the rod from the pull-off to shorten or lengthen it. Usually the vacuum diaphram on the pull-off just fails, and by simply screwing on a new one, without modifing the rod length, will fix the problem. Another overlooked adjustment is the choke unloader. This is the mechanicial foot on the throttle shaft that opens the choke plate to a much larger clearance, in the case of extreame flooding. If the engine won't start cold, there is no vacuum to open the choke brake, so this device is used to clear a flooded motor. Another thing to keep in mind is it the throttle linkage won't open the throttle plates completely, the choke unloader won't work. Checking your linkage for proper wide open throttle, will give both tremendous horsepower, and better cold starting.