Apropos of nothing at all, that 178mm is exactly the spacing on the action bolts of the Tikka M595 (.22/250 - .308 medium length) which preceded the T3.
Tikka moved the trigger assembly closer to the magazine-well with the T3, so while it's the same action length for .222/.243/.30-06 calibres it's actually shorter than the norm.
The M695 (long action) spacing is 192mm which fits your bill.