Seems to me you are missing out on an opportunity to buy a new rifle.
My favorite antelope rifle was a Wby Mark V in .7mmm Wby Mag, shooting 134 gr Noslers, but anything in a flat shooting caliber, with a fast opening bullet would be ideal IMO.
Being overgunned, although fun, might result in wounding secondary animals unless you are careful at picking your shots.
Today, I would lean towards a .243 just for the fun of it.
BH63
