You might check and see if your chain is worn out. What rear hub do you have and how many teeth?
My Speedster is 2 speed kickback, 18 teeth, and has the same chainring you have. With a new chain, depending where you cut it, the axle can be either almost out the front of the dropout, or almost all the way back. Anything else requires a half link. I seriously doubt the factory screwed with half links much if any.
It turns out the axle should be way forward. Apparently Schwinn intended it like that. There was a thread recently about a Corvette, derailleur equipped, and it turns out that the axle winds up way forward like that, and on a derailleur bike you don't have to slide to tension the chain. Since then I have been paying attention to Schwinn middleweights when people post their serial numbers. On 1-2-3 speeds the old marks made by the axle washer are always way forward. There could be exceptions, but so far its been 100% since I have been watching.
You might just need a new chain and possibly one less link.
EDIT: 67 Panther from another CABE thread:
View attachment 1321835
.