Great!
Now (I hope you have the cycles for this) we need to introduce modulation.
As you mentioned the position of the taps have a large impact on the coloration of the reverb. To reduce this, the taps should be randomly modulated within a 5 ms window.
The modulation should be random as opposed to a chorus pattern. This can be accomplished using a table of random offsets. The taps can be moved using linear interpolation with at least 16 steps between samples. Use the table to define a new offset for whichever tap finishes it's traversal during the current sample time processing.
Play with the speed of the tap movement (and the resulting pitch effect) to meet your subjective taste.
It's going to start sounding nice now, but there are a few more steps to consider and a lot of tuning to go.
-Casey