As far as I can tell, nothing is broken in the current system (of LaTeX or of TextMate). I just wanted to experiment with a different way of doing things.
If there's one thing I've learned about LaTeX it is “don't try to change anything.” Or maybe “change things at your peril (you will die).”
But if you want to add \begin{sect}{} to the symbols list have a look at the Symbol List preference item. You add a regex clause to the symbolTransformation variable to match that form. One drawback will be that there's no way to figure out the depth of the current section... Something like the following should work:
s/^\begin{sect*}?(?:[[^]]*])?{(.+)}/ $1/; # \begin{sect}
As for modifying the Show Outline command... I don't think a simple modification will suffice as it is based on the same regular expressions that the Symbol List is. You'd have to rewrite the whole thing maintaining a stack to remember how deep you are...