Zinc content is most important during the initial camshaft break in. After that it would always help, but not required.
Synthetics will allow you to drive longer between oil changes versus traditional dino juice, but in older vehicles I personally don't see that big of a difference. In newer vehicles that are engineered with much more strict and exact tolerances it really does make a (noticeable) difference. That said I usually do run a synthetic blend in my Bronco, which I haven't changed in 2+ years and it still looks like new. (I should probably change that sometime soon, but it's only been 3500 miles...%) )
I have never owned a vehicle that burned oil 'ever', so I would assume if that is the case you most likely have other issues aswell. I guess I should take that back, I did have a Chevy I drove at work that burned a quart every 1000 miles, but considering the whole drivetrain had a severe meltdown at about 30,000 miles I tend to think it was a total POS... I used to run air cooled VW's very hard and they didn't even burn oil...