WKHL is a Class A station, which means they can only run 6kw at 356 feet. If they raise the tower higher, the power has to be reduced. They are currently operating at maximum power for their class, so "cranking it up" is not an option.
If Cox wanted to be an oldies player in NY, they could try to buy up some other frequencies and ring the city with a simulcast. I beleive they already have a couple of stations on LI, so they would probably need something in Central NJ to round things out.
They could also move the oldies format to 99.1. Problem there is that although 99.9 is a Class B (max 50kw @ 500 ft.) their transmitter is farther away from New York. They still fall a bit short of Manhattan coverage-wise and you can forget about NJ. Unlikely, but technically do-able would be if they also acquired WAWZ, also on 99.1 and simulcast with a synchronized signal. That would cover most of the metro area.
One note on maximum power limitations.... In Zone I (which encompasses most of the northeastern quarter of the US and is roughly bordered by the Mississippi river to the west and the Ohio River and then extending along the VA/NC border to the south... with the exception of those portions of NY, VT, NH, and ME north of a line that is roughly on the latitude of Rutland and Portland.... plus all but the extreme northern part of California, and Puerto Rico) the most powerful stations permitted are Class B.
The rest of the US is Zone II, which encompasses the rest of the US. In that Zone, the most powerful stations permitted is a Class C, which can operate with 100kw at 2000 ft.
You will find some exceptions.... all "grandfathered" stations that got approved before 1962 when the current rules went into effect. That explains the 320kw station in Grand Rapids, MI and the 175kw station in Columbus, OH, among others.
