Your choke is still operational, though, isn't it (opens all the way when warm). What type of choke do you have? If it's factory and it isn't electric, then it's hot air thermostatic type, which means you can simple loosen the coil cover and rotate it counterclockwise to increase tension on the choke flap (same as adjusting an electric choke). Some coil covers were riveted from the factory, which mean you'll have to remove them first and tap the holes to accept screws. Make note of any adjustments you make by using the tick marks on the aluminum choke housing.
It is unlikely that your choke rod/linkage is to blame. They are always a little loose.