Hi there,
I'm also in more or less the same position as you guys. I never had really formal lessons, but learned somewhat from family and such who knew a little bit. Like you, I can play a few pieces that are pretty far ahead of what I can sight read comfortably, but I've made the decision to practice sight reading almost exclusively every day until I bring it up to speed.
One thing I will tell you is that it will be a humbling experience lol. You have to really start from the beginning. I figured that since I could play a few more advanced pieces that I would be able to start sight reading at least at half that level. I was wrong.
In order to really see some good improvement you have to go back to a level where you can sight read a song straight through with roughly 95% accuracy. For me, this was seriously elementary level stuff (i.e. only in C major, no hand position changes, and mostly quarter notes and slower).
The important thing is to take everything in slow chunks. Don't expect to be able to jump into pieces that are in, say B flat major with complex rhythms and jumps all over the keyboard. Start off with the really easy stuff in C major, then slowly add stuff with simple position changes (i.e. from middle C position up to C5, or simple key changes to like F or G major), and keep building on as you master each new concept (i.e., don't try to skip over anything until you're able to sight read through a few new pieces in that difficulty level with like 99% accuracy at tempo or close to it). Also, play a lot of music at each new concept level. This really helps your pattern recognition and helps you get used to new pieces faster.
I don't know if this is a possibility for you, but something that has helped me a lot in my sight reading has been using the game Synthesia along with the learning pack (lets you play with sheet music instead of the guitar hero-esque bars) and a midi keyboard. It really helps with the whole "not stopping" thing, as it forces you to keep going if you screw up (much like guitar hero or stepmania and the like), and it gives some feedback as to whether you're hitting the right notes (a big plus for me at the beginning so you don't have to look down and check if you hit the right note every time). The learning pack add-on costs $15, but I think it's worth it (imo the guitar hero bars themselves are useless, I want to learn to sight read actual music notation instead of relying on a proprietary computer program to learn new music lol).
I've been at it for about a month now, and I'm still pretty terrible, but I've made measurable progress and I'm pretty excited about it (went from barely being able to read a simple C major melody in one hand to being able to comfortably read most easy melodies and chords hands together at tempo or a little under in C, G, F, and D major with 8th notes (as long as there aren't too many

), and some not huge position changes (they're my biggest obstacle atm).
So basically:
1. Start at the lowest level you can comfortably sight read at tempo (which might be lower than you expect) and work from there.
2. Add new concepts one at a time and master them before moving on.
3. Don't try to skip ahead in concepts before mastering them; you need all of them.
4. Go for quantity over extreme quality (i.e. don't try to polish every piece. Get it to where you can play the notes at tempo with accuracy and then move on to the next one).
Hopefully that helps a little. Keep at it, and good luck!