I use blankets instead of sheets - the frost won't soak clear through when it melts.

A C9 christmas tree lamp is 9w bulb, Individually not much heat which is good wont burn your tree, and all you are trying to do is keep the tree at or above 32 that will keep it alive . Put a string of 50 you are supplying almost as much heat as a 500w lamp. Put a thicker blanket or frost cloth to protect against frost burn thats a different problem..

Here is a link that might be useful: What causes frost

I use Agribon floating covers and others similar. They are very light and protect against frost and, in cases, freezeing. I've had it protect young bean plants down to 28 degrees. I also have had good results with blankets.

I believe what caused your freeze damage (tip burn) was from the sheet touching the leaves. If possible build a small structure that you can drape your blanket, frost cloth, etc. and as much as possible avoid direct contact with the leaves. Also when I use sheets ( I prefer the thicker frost cloth like Agribond that shuffles mentioned...I've also used several layers of sheets to give a thicker protection when I run out of old comforters, blankets. The thicker the cover the less likely it will soak through and freeze the leaves/branches.

Something like this you can build using either PVC or electrical Conduit works well and pretty easy to construct.