Why does the motor feel jumpy when I take my foot of the gas?

Yes it does do it in reverse if I take my foot off the gas The car jumps and jerks several times before slowing.

Can you attempt to put it in gear, E brake off, and push the car, rocking it while watching the engine/transmission to see if there is movement in the mounts. The more severely the movement the easier to spot the mounts if they are bad. If not sure compare it to another vehicle of the same style, that is not showing the same symptoms, so you can judge what movement yours should be.

3rd gear and just cruising along in suburban street. So, if I take my foot off the gas there's noticeable jumping which can be felt, and also felt up through the gear shift. Also, if I go quite fast in second and then take my foot right off the gas it does the same thing, i.e. jumps and jerks before it begins to slow.