Black smoke and oil consumption

2000 Corolla LE (5 speed) 1.8L engine has 119k miles. Purchased a few months ago and have had several latent problems repaired by dealer (Catalytic converter replaced 9 weeks ago and Variable Valve Timing gear replaced 6 weeks ago). Check engine light came on for both problems above, but it is not on now.

THE PROBLEM -

Car is using oil fairly rapidly and burning black smoke. (Don't know exact amount but probably a quart every few hundred miles or so.) There are no visible leaks. There doesn't appeart to be much if any smoke in the exhaust when idling or when cruising but revving the engine up to 5k rpm or so produces substantial black smoke. (This could have been happening even before the VVT gear swap, but I have no way of knowing).

The car runs smoothly and light acceleration is not a problem. It does seem to miss a bit during moderate-hard acceleration, but it isn't terribly noticeable, and I just chalked it up to the small engine size and mileage.

Is there any reason that the VVT gear replacement could be the instigator of this problem? If not, what would be the most likely cause(s).