You are attempting to chill the line with the beer. If you do not mind the cost of this practise, then you would be fine less a lot of foam until the beer from the keg cools the line. This often is referred to as the most expensive dispensing system available. A beer chilled system!
You should change your line. If your beer temperature at the keg is 38F and you have a 2.6 v/v product, then continue to dispense at 14 PSIG. Your gravity from the bottom of the keg to the faucet would be approx. 14' This results in seven pounds of resistance. Throw in another pound for hardware and you are now at eight. If you can handle a gallon a minute flow rate, you will still need six more pounds in beer line that is approx. 12 feet long.
A combination of 11' of 5/16 ID vinyl attached to one foot of 3/16" ID vinyl will get you close. Maybe slightly slower than 128 oz. / min. Get a big bucket! You will need it for all of the foam until you can maintain temperature between the keg and the faucet.
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