I have a number of ARs in 6.8SPC and would love to complement them with a lightweight boltgun in 6.8SPC. Sadly - if you want a lightweight bolt gun, you must make it.
Remington offers occasional runs in their 700 line, with the emphasis on heavy and long barrels and preudo-sniper visuals. Nobody else has anything on the market right now.
You can make a Savage short-action in 6.8SPC, but the action will still be long for the chambering and you'll need to find somebody to muck with the boltface and extractor to fit the rim of the 6.8SPC.
I have seen reference in this forum to a custom CZ527 in 6.8SPC, but that was likely a very expensive custom piece.
If you want to make one, I would recommend finding one of the Zastava mini-Mauser actions (now the Remington 799 thingees) and using that as a baseline. Starting with the miniMauser would eliminate the need to block the magwell for the shorter round, and would leave rebarreling, opening the boilt face, and relieving the extractor as the only real chores.