Early A bellhousing in 68 A body

Slip yokes started in '66.
If it has a 26 spline output shaft, its a '66-'67. If it has a 30 spline output, it's a ('67 big block, or) '68 and up.
The bellhousing number means it's for a '64-'66 A body.
The two being paired together suggests that it was original to the '66 Dart.
It will live just fine behind a mild DD 360, especially if you upgrade to the 10" scalloped disc and pressure plate.
The issue is going to be the balance; that flywheel is for an internally balanced engine, your 360 is externally balanced. You can either have the flywheel rebalanced for a 360, or run something like this:
Quick Time RM-531 Quick Time Balance Plate - Mopar
The linkage you'll be on your own with, usually people are swapping from the early 122 tooth flywheel to the 10.5" 130 tooth flywheel and bellhousing, you're proposing going the opposite way- not saying it can't be done, you'll just have to be ready to modify and fabricate. I also hope you've already got three pedals in your '68, because the pedals from the '66 are completely different and won't work in your Dart.