reasons to keep your MTB:
- you like the gearing (road bikes typically have a narrower range of gears)
- it's bombproof
- you occasionally ride muddy (but not necessarily off-road) places where the bigger tyres and tyre clearance are advantageous
reasons to change:
- the MTB is slow and heavy
- a bike with narrower tyres and mudguards will get you & your stuff less wet in the rain
Make a list of your criteria and prioritize them. If 'bombproof' is at the top of the list, I think you've answered your own question. Otherwise, don't dismiss a tourer out of hand. You may find that it will come closer to one-bike-does-it-all than most others. However, I will add to your confusion by suggesting that you consider an Audax bike. Many people find them a good compromise between 'full-on tourer' and road bike.
You can check the CTC site at
http://www.ctc.org.uk/DesktopDefault.aspx?TabID=3788 where they explain the differences between different bike and associated types of cycling. I think you'll find the information there helpful.
But, the best thing you can do is ride some bikes. Try bikes at the bike stores near you. Hire bikes so you can ride them a bit longer. Don't make a decision until you've evaluated the alternatives as more than a picture in a catalogue. If you find one you like, look for a similar used one. If you don't, invest in a second set of wheels for the one you've got.
I would avoid new road bikes in your price range. The cost compromise is generally in shifters, drivetrain, and wheels. While the cheaper gears and chains are usually okay, the wheels won't take much abuse (like potholes and kerbs) and the shifters require frequent maintenance.
Good luck!