I'm sure it would. The A321 can operate from Luton (runway length 2160m), Leeds-Bradford (2190m) and even Belfast City (1829m).
I've had another look at that BD134 descent, and you can see that between the Murco petrol station and your house, the plane stops descending but the speed remains the same. That means that there must have been an increase in thrust at that point. Although BAA say that it's up to NATS to decide on the approach path for any aircraft, any late join to the runway heading will inevitably result in more noise at lower heights than the normal approach. For safety reasons it's not desirable to put too many constraints on NATS, but in this case with hardly any other aircraft around, it just looks like a convenience rather than a necessity to route the plane that way. Perhaps a complaint to the CAA should be made rather than to BAA.
I agree with Jonathan that it's worth experiencing the noise in Grove Park to get a better feel for the typical level of aircraft noise under the normal flight path.