The JB jr is a fine pickup, and you may as well try it. The full sized JB is the hands down most popular aftermarket pickup on the market. By a LOT. Certainly, I sell them probably 4 or 5 to one over anything but the Seymour Duncan Jazz, and even there it is still 2-3:1. Given SD's
21 Day Real World Return policy (God, I sound like I work for them. I don't, but I do sell a lot of their pickups, and I like them a LOT), there is no reason not to at least try the thing. In essence, you have 21 days from when you buy a SD pickup to decide if you like it. Just don't cut the wires short until you decide you're going to keep it. (I don't much care for that part, but you can't fault them for wanting to be able to resell the pickup.) If you don't like it, bring it back and they will replace it with another pickup of the same value. So a decent job at the soldering, though. You are supposed to have them installed by a pro, but as long as you do it right that shouldn't be a problem. It is, at any rate, a hell of a good offer, on their part, and one of the reasons I like SD so much as a company.
If you wanted something a little more traditionally Strat sounding, though, one of my absolute favorite pickups on the market right now is the Seymour Duncan Classic Stack Plus. Dead quiet, and they sound like single coils (well, 98%). They are also designed so that, in your "in between" positions, you can wire them up to split the coils and get 100% of the way there, but still be quiet. I have a set in my Strat, and I can't seem to put that guitar down, even two and a half years after I finished it.
Also, there is no reason you couldn't put the Little `59 in the bridge position - it just isn't a common choice. It isn't that much work to try it, and you might even like it.
Gabriel