I went to www-car-part.com and plugged in your truck and selected DRW, Cab & ch, (w/body code F37 & F38), Spicer, 11,000 GVW (70HD, 4.10 ratio) And this came up.
1985
Rear Axle
Ford Truck 350 111,998 A VA4344 $550 Virginia Truck Parts USA-VA(King-George) E-mail 1-800-390-2025
I then selected a later model which should fit, this is still a cab and chassis rearend.
1988
Rear Axle
Ford Truck F350 CHECK RATIO 123,569 A CC3588 $850 Estes Auto and Truck Parts USA-VA(Pilot) E-mail 1-877-616-4900 / 1-540-651-4637
1997
Rear Axle
Ford Truck F350 DULLY F0340 $750.25 Phoenix Automotive USA-VA(Culpeper) E-mail 540-825-2571
The cab and chassis rearend may be a challenge to find, a dually pickup rearend will not fit if you really do have a cab and chassis truck. To tell you the truth, I like the transfer case idea. You will need to buy a tranny AND a transfer case, but you can't beat the low range the transfer case gives you, it's really handy when you are backing up. You do not have 4x4 but who cares? And you could put a front axle under it at a later date if you wanted.
Here's a 4x4 4 speed.
1987
Transmission
Ford Truck F250 6.9,4 SP,4x4,Tilt,CRUISE,Floor 152,124 A D08587 $350 Estes Auto and Truck Parts USA-VA(Pilot) E-mail 1-877-616-4900 / 1-540-651-4637
1987
Transmission
Ford Truck F250 BOWIE/ CUSTOMER OWNED244-8614 ,STOCK NO. #023856 #023856 $Call Roger's Auto Sales & Used Part USA-VA(New-Market) Request_Quote 540-740-8733 / 800-377-8302 Request_Insurance_Quote
Here's a transfer case to go with it;
1985
Transfer Case
Ford Truck F150 4.9,4x4 102004 $350 Estes Auto and Truck Parts USA-VA(Pilot) E-mail 1-877-616-4900 / 1-540-651-4637
1985
Transfer Case
Ford Truck 250 NEW PROCESS, SLIP YOKE OUTPUT 0 A 11168 $350 Shenandoah Auto Salvage, Inc. VARA USA-VA(Stuart-Draft) Request_Quote 1-540-943-2300 Request_Insurance_Quote
1986
Transfer Case
Ford Truck F150 CK-SLP-O/PUT-SHFT VA0954 $300 Virginia Used Auto Parts USA-VA(Suffolk) Request_Quote 757-539-0520 Request_Insurance_Quote
1986
Transfer Case
Ford Truck F150 slip yoke output,STOCK NO. 003036028 101,386 A 003036028 $225 G & B Auto Parts, Inc. USA-VA(Floyd) E-mail 1-540-745-7401
1986
Transfer Case
Ford Truck F150 STOCK NO. #1072 #1072 $150 Greear's Used Cars/Parts, Inc. USA-VA(Coeburn) E-mail 1-276-395-3321
1986
Transfer Case
Ford Truck F150 GREY LONG BOX 4X4,STOCK NO. 000720029 000720029 $150 Greear's Used Cars/Parts, Inc. USA-VA(Coeburn) E-mail 1-276-395-3321
Of course you will need a driveshaft to go with it if you go the transfer case route.