My truck did the same thing--('82 k2500 GMC,6.2/TH400)...
There is a vacuum regulator valve (VRV)-mounted to the injector pump,that controls the amount of vacuum supplied from the vacuum pump,to the modulator on the tranny...if its defective or not adjusted right,it will throw off the shift timing,usually drag them out and not shift until its going faster than normal...mine refused to shift into second until 30 mph,and third at 45-50 mph,and it slammed in hard too....
My VRV valve was junk,it had busted in two--a search for a new one proved futile,and every 6.2 truck in the junkyards I find always have a 700R4 tranny,so I have had no luck finding one...(nor would I be able to pay for a new one if I could anyway)--to get the truck useable I called a local tranny guy,who said I could run the vacuum hose from the pump direct to the modulator,and said I should screw in the little adjustent screw inside the modulators vacuum hose nipple until it gently "hit bottom"--my tranny now shifts a bit early,but at least I can get it in third by 25 mph instead of 50!..
A gas engine has its higheat vacuum at idle,and it dies off as the throttle is opened and rpm's increase--with a diesel,it has a vacuum pump,so the faster it spins the more vacuum you'll get...the modulator uses vacuum to regulate the line pressure in the tranny--I was afraid by delivering full vacuum to the modulator,it would reduce line pressure (like a gas engine would at idle),and possibly cause slippage or burnt clutches--the tranny guy claims adjusting the modulator like he said too prevents it from being able to lower the pressure to a harmful level--at any rate,after 6 years of plowing abuse,it still shifts good without slippage..I'd prever to have the VRV valve hooked up and working though!...
They do sell cable operated vacuum modultors for vehicles with superchargers,as they wont have the correct vacuum signal like a stock engine would..costs over 100 bucks and dont look like fun to hook up and get the cable adjusted right though...