@KeithB
I manipulated your photo to show you where the issue is. At the extreme lower right the reverse lever is just barely visible. I enlarged it in an inset for a little better detail as to the part everyone's mentioning.
Make sure the car is secure (won't roll) and the transmission is in neutral. Note and keep track of any washers during disassembly so it goes back together the way it came apart.
Remove the linkage rod's retaining clip or cotter holding it to the transmission lever and drop the linkage rod out of the way. Remove the nut holding lever to the transmission and flip or rotate the lever 180° and reinstall the nut. You'll almost certainly have to adjust the linkage rod's swivel. Thread it whichever direction is necessary until it easily goes back into the lever with the three shifter levers aligned. Make sure they're aligned!* It should now look like the lowest rod in
@Oldmanmopar's photo. Reinstall any washer(s) and the retaining clip/cotter. Done, and reverse is now forward as it should be.
It'll be obvious once you're under the car, and should take maybe 10 minutes. It's literally one nut and one clip to remove and reinstall and a bit of adjustment on the swivel.
*Hurst shifters have a built-in alignment pin setup, which consists of notches in the shifter and holes in the levers. Most, but not all factory Mopar shifters are drilled through all three levers. If yours are, use an appropriately-sized drill bit (snug, I don't remember the size) and push it through the slot and all three shifter holes to keep them aligned. Wiggle the levers a bit until you feel the bit go through the notch on the transmission side of the shifter. See below.
If your shifter is the oddball and you can't use the drill bit, get it close and check the action of the reverse gate (not reverse gear, just full leftward travel in neutral) sitting in the car. There should be a firm detent but it shouldn't be hard to engage. Unless you have the Miller special tool, getting it right can be a bit of trial-and-error. If you have to put forward pressure on the handle to get into the reverse gate (again, not reverse itself, just that part of the shift pattern) thread the swivel toward the shifter and try again. If you have to pull back a little, go the other way with the swivel. On my two A-body shifters, the levers are aligned along their back edges with the drill bit in place, so that's a fairly good indicator that you're close.
I hope this helps!
