bad city milage 2bbl

Forgive me for disagreeing, but the drop the ballast will not make a terribly dramatic change, regardless of the ignition type, and would not normally cause a serious mileage drop. The charging current into the coil is what sets spark energy, and the ballast will lower it's resistance somewhat equalize the drop in voltage applied to the coil+switching circuit.

If it was 3 volts drop, THEN I would agree that it would be the place to first focus The voltage drop ought to be corrected at some point but is not what I would focus the OP on at this time for his poor mileage. Timing is much more important for him to tackle at this point.

As for the battery, OP, after you have driven the car around for about 30 minutes (to let the alternator do what it can to charge the battery), check the battery voltage across the battery terminals with the engine running at a fast idle. It ought to be up in the 13.7 to 14.3 volt range. If much lower, then either the battery or alternator need attention.

And, OP, a toasty hot ballast is normal.