I've struggled with this limitation and I've discoverd that if you can't invest in propane, you've got to invest somewhere else, and thus far my trials have shown that, if at all possible, you should look at your options for kettle dimensions more so than the limitations of your stove when you're stuck working in apartment conditions.
I'm in a 1 bed, 4th story apratment using a Premier 20 inch gas range, which I believe is one of the smallest stoves on the market. I have no issues getting 7-8 gallons to a rolling boil in under an hour from room temp if only because I've selected a 10 gallon kettle as wide as my stove so I can place it over all 4 burners.
I found that after insulating the pot with a shielded fiberglass blanket that I only need two burners to get a boil. I plan on using sheet-metal angle stock on the low-side of the pot to retard the flames so it's safe for me to use on the gas range.
As far as cooling goes, you can probably speed up the process by adding salt to your ice/water mix and agitating. My system is like a reverse immersion cooler. I run hot wort through copper tubing that is submerged in an ice/salt mix that I stir up as it runs through. The salt forces/expediates the chemical melting process, which speeds up heat absorbtion beyond it's normal rate, which in turn creates a very rapid drop in temperature that often surpasses the freezing point of water without actually without forming ice.
If you just want to keep it simple, throw 3-5 cups of salt in together with a bag or two of ice in your sink and a gallon or two of water. Stick your kettle pot in and stir the ice/water/salt mix for a few minutes. You should see a much more rapid drop in wort temp there.