FriendInFlatbush – Unfortunately your gross oversimplification is not correct. As zahavasdad stated the Solar Leap year is to correct the roughly 1/4 day extra every year. No connection at all to the Jewish calendar, and only corrects itself, not the missing days in the 19 year cycle.
Rosh Chodesh Adar Rishon always has two days, it does not vary. The only months that vary are Cheshvan and Kislev (i.e. Rosh Chodesh Kislev and Teves).