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Yes, any transmission that will bolt up to a 302 and 351w V8s will bolt up to the 300 six. Bell housing, etc it's all the same.
The two most common 5 speeds are the M5OD-R2 and the ZF5. The biggest issue you'll run into is that they're both hydraulic clutches so whether you currently have an auto or manual now won't matter as the manual in 81 was a mechanical clutch and you'll need to mount the hydraulic master cylinder to get them to work.
It also requires swapping and relocating the crossmember. Both 5-speeds are longer than a T-18. Which means a shorter rear and and longer front driveshaft as well. Try and find one with the transfer case and shifter intact. You'll have to cut a hole in the floor for the shifter so get the transmission access panel from the donor truck too.