If you want to add reverb to your signal, then you need a reverb unit.
There are two ways to approach this. You can use a standalone reverb unit, or you could use a plugin running on a computer (as well as an audio interface to get audio in and out of the computer). The computer gives you more flexibility, but it also gives you more latency (that is, plugins on a computer will have a few milliseconds of delay). A standalone reverb unit has the advantage of much faster boot times, less chance of crashing, and typically much lower latency than a computer.
Reverb units range from minimalistic "pedal" designs intended for guitar players up through large multi-part rack systems. Personally I find the sweet-spot to be in the 1U rack mount units. There are a ton of great digital reverbs from the last decade or so in the $50-$200 range out on the used market. The Eventide Space is also excellent, but its sound may be too artificial for you (I love it because of its "unrealistic" patches).
AVP isn't about recommending specific gear, so your next step (after deciding whether to go with a hardware reverb or a software plugin) is to go read reviews and listen to the various units out there. I find that Lexicon tends to make more "realistic" reverbs than some of the other brands out there, so that may be a good place to start.
AJ Henderson makes a good point, though. If you want your realistic reverb to sound good you need to feed a great signal into it. I agree with you that the D50 has excellent microphones, but those same mice will pick up a lot of the ambience of the space you are in. You want to feed a dry signal into your reverb for best results. However, if you run your signal into your reverb unit and then play it in a concert hall, you will get the hall's natural reverb on top of yours.
Actually solving your problem probably involves some study of acoustics and a lot of experimentation. You may have better luck hiring an audio engineer with experience doing this kind of thing.