I' d leave the 788 alone and try to grab the Winchester featherweight in 6.5 X 55...what a sweet whitetail gun that would be!
I think by the time you had a ready-to-fire barrel installed on your 788 you' d have at least $150 dropped into your 788. Course, if the 243 really isn' t a shooter...changing out the barrel would be the cheaper way to go.
But, my way of thinkin is...can' t have enough guns!