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As an earlier poster said Street glide shocks are 1 inch shorter. I have a Road King Custom which also has the 1 inch shorter shcoks from the factory. I like the handling of my Road King Custom better than the Classic and Standard my buddies ride. I have a set of 11 1/2 inch Progressive shocks removed from a used Road King I am setting up for a 6'4" friend I would sell for $100.00 shipped with PayPal. They are the 412s in Chrome.
The cheapest thing to try first is a lower seat. If that doesn't do it then Progressive makes all the lowering items you will need to lower the bike front and rear. Keep in mind these bikes were designed for a certain ride height. So when you lower it you will change the handling characteristics of the bike.
I agree with trying a lower seat first. I had my FLSTC lowered and the ride and handling was horrible. I raised it back to stock. I know a touring bike and softail are two different bikes, but lowering it will affect the ride.