At 38F with Coors Lt. carbonated to 2.75, you would require 18 PSIG at your elevation. Since you adjust one pound for every two degree change, you would apply 16 PSIG. The 10' of 3/16" line will be more than enough as you probably have a slow flow now.
Preferably, to maintain carbonation at the keg and as you dispense, you would strive for the same temperature from the keg to the faucet. With out cold air circulating in the tower, you will always have an issue with the first pour. If you can live with this, fine. To reduce the amount of foam, dump the initial amount that pours out of the faucet and then start with clear beer. If you try to pour clear beer over the foam it is over and you will end up with a mess.
Conduct a search for cooling tower. There are a few great set ups that are successful for the users.
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