First, 6 feet of line is simply not enough. I'd start with a minimum of 10 feet. But 12 feet would be even better.
Mostly, the problem is the force carbing rapidly like that. Think about a bottle of Coke. Shake it hard and open it. That is pretty much what you did with the beer. That's why burst carbing like that doesn't usually work.
Normally, a good way to carb up a beer is to put it at 12 psi at 40° for about a week or two. That works perfectly each and every time.
If I am in a huge hurry, though, I will put it in the kegerator (absolutely no shaking!) at 30 PSI for 36 hours. Then purge the keg and reset to 12 psi. In three days it is very nicely carbed and clear as well without a lot of sediment suspended in it.
It really is nearly impossible to carb up a keg of beer nicely in 24 hours. Oh sure, it can have carbonation, but that doesn't mean it will won't be foamy or full of sediment or even taste as good as it will in two days.
Since it was shaken at 30 psi, it is over carbonated. The only fix for that would be to take it off of the gas and purge the keg as often as you can. Once it is no longer over carbonated, it can be put back on the gas at 12 psi and 40°.