The Insert jack on Input A takes the signal from the Input (after you have added any "distortion" effects) feeds it via one arm of the Y connector to your reverb and returns the signal for recording through the other arm of the Y connector. Provided your reverb unit is providing enough output gain, you should record your input with reverb added. The Insert jack "breaks" the circuit between the pre-amp and the A/D converter for an effect loop to be put in (as you have done) Whatever is fed back through the Insert jack should be recorded. I suggest you set up without the reverb in line and check you are recording OK then repeat the exact process with the Y connector and reverb inserted. You do not say where you are monitoring the final recording. If it is through the MR16 headphone jacks then you should be recording what you are hearing.
My method would be to record the "raw" (no reverb) material on to, say, Track 1 and then set up the MR16 to output Track 1 to Aux Out 1. Patch Aux Out 1 through your reverb unit to Input A and re-record to, say, Track 5. (Once the signal has been converted to digital - you will not lose quality) Because the MR16 runs all its 16 tracks together w.r.t. time, you can re-record each track seperately. Example:- Track 1 through reverb to track 5 and track 2 through reverb to track 6, then use tracks 5/6 to mix down. This may give you more flexibility.
I guess that the echo facilities on the MR16 are not what you are looking for!
I have "patched" directly from Aux Out 1&2 to Inputs A&B in order to play with the 33 Input Eq settings in the MR16. Using Aux Out to re-record you "raw" material is one of the more useful options on the MR16.