Yowza! Good for you! Hope you figure out that shifter ASAP.
I weigh the same as you... but I am FOUR foot 11, not 5 :-). I pull a trailer loaded with toddlers and gear that probably gets close to that, but I've never done more than about 7 miles round trip. The children, of course, have to ride in the front part of the trailer (well, middle, I guess), but I have been fortunate enough not to get a flat. I'm with you--I love me some first gear when I'm pulling all that load :-).