Howell,
Welcome to GB's.
Don't have a Handi in 243 but most here are happiest with 90gr and under bullets. The throats are long but the case shoulders are still normal specs.
I think for consistancies sake I'd keep the cases trimmed to factory specs and not worry about the long throats. It really doesn't seem to hurt accuracy on most of these rifles.
I know it hasn't on my 223 UV.