This technique also works with Rapture, which opens up even more possibilities.
... like pitch envelopes. DimPro has them as well, but limited to +/- two octaves (with Rapture at +/- 8 octaves).
Load the clip, set the Pitch EG to On, and the Depth to -9600 cents (to pitch downwards in the extreme). Set the Sync multiplier to something huge (like 128) for starters, and right-click another node in the upper righthand corner.
This kind of approach allows to to fine-tune the "tape-stop" rate and taper by simply dragging around the segment between the 2 EG nodes. A copied & pasted envelope to the AMP EG can control the volume of the effect.