10 PSI at 48F will give you an undercarbonated Dead Guy, (way to go OP for using the calculator!). 16 PSI at 48F sounds right, (I shoot for 10-11 PSI at 37F, for reference, on most of my ales), and you are correct, you DO want to serve at 16 PSI so you don't lose carbonation over time! You can certainly do Stuntmantoo's version of carbonation, which for you would be 30 PSI for 24 hrs, then down to 16, but that's riskier than the "set and forget" method. Personally, I DO use a similar method to Stuntmantoo....I do 48 hrs at 34 PSI, (with the keg starting at room temp and cooling in the fridge during those same 48 hrs), then down to 10 PSI to serve...but my fridge is colder, hence the 10 vs. 16 PSI.
Your biggest problem is, as you guessed, line length. I like about 1 ft 3/16" line per PSI. I have 10' 3/16" for my 10-11 PSI setup, and 35' 3/16" for my 35 PSI setup (soda), and I get great pours. They pour a bit slow, (yes, the longer the line, the slower it pours!), but you have exact control over foam. At the end, if I don't have enough head in my glass, I just half close the tap, which causes the last few tablesspoons of beer to shoot out and form a nice head.
tl;dr: Get longer line! 10 feet at least.