My HSS has the stock trem in it, no LSR nut and stays in tune really well. If I had to upgrade it though, I'd think about one of these......GuitarFetish

Another thing to consider is if you need a trem in the first place. If you don't do any divebombing and things like that, you could even get by with a hardtail bridge. For that matter, you could dispense with the LSR nut and get a little cheaper guitar.