Hi Todd,

I have a Strat too and find problems with the high 'e' string doing that. When I stick the string throught the 'tuning peg', lets say there's 1/2 inch sticking out, I'll bend that at an angle to try to make some resistance..like if you were hammering a nail and just bent it over.
Then I'll wrap the string around the peg a bunch of times like I was winding a spool of thread, when I run out of string to wind then I get the string winder out and finish off the job while holding the string tight with my right hand. I don't know if I explained this very well it's easier to show you, hopefully it helps some.
Our guitar tech Steve White is available too if you'd like to ask him under 'ask a guitar tech'.