Please take this information with a grain of salt
, operated some straight 200's several years ago, for the aircraft I used to fly you are correct concerning the current limiter problem, Because of the initial draw when you hit the starter you would expect to burn one out in one or two starts and at the very least cause some arcing, electrical systems may have been modified since I operated. We had a pretty sharp engineer on staff and we modified our procedures, we had a Christie sp battery charger and kept our ni-cads in top shape, instead of following the Beech procedure we fired up #2 and immediately followed by starting up #1 (or visa versa, long time ago), when the second engine hit about 12% we turned on the first generator.
This procedure only cycles the batteries once, your batteries must be in top condition and you can't go in and listen to the ATIS and get your clearance prior to using this method, this will take the top charge off your battery.
Good flying, the 200 is one of my all time favorites!