Nothing wrong with the 6.5 swe... Except for what you want to do, the .223 would be better. They are so cheap to shoot, you'd shoot it more, and all that can do is make you a better shot with that gun.
Many years ago, before the Valmets, i moved up from the cheaper Savage combo's to there 2400 model (Valmet mfg'd pre 412 models) in 12/.222 Rem.. I swaged my own bullets out of empty 22 caseings and did a lot of small game hunting with that .222... I harvested a lot of rabbits and ptmargian for my freezer with that combo.. I swaged the bullet "backwards" so they would be solids, and then loaded them to about 1,700 fps...
I still have it, and i've been thinking of getting it out and shooting it again. The .222 bbl. is really a tack driver, and it would be handy around the shop as at times a shotgun would be usefull to make up for my ageing eyes... hahahahaa
Anyway, happy shooting and keep us posted!!
Drilling Man