I had a TH350 --did the same thing...
The TH350 in my 72 K5 I had years ago would not go into "drive" first thing in the morning after sitting overnight..took 5 minites or more,longer in cold weather...I tried every additive they had out at the time,tranny filter and fluid changes,new modulator,etc..nothing helped!....after it finally shifted into drive,I could drive it hundreds of miles without a problem,it shifted nice,no slippage,etc...reverse worked instantly!-

-I could back out of my parking space and into the street--then I'd have to PUSH it off to the roadside and wait several minites--as soon as my temparature gauge read normal,I'd feel the tranny lurch into drive,and off I could go...
I had several tranny shops check it out,one said the "lip seal" on the forward clutch was hard and brittle,another guy said he thought it might be the valve body,since I drove it 2 years that way and hadn't smoked the tranny yet...I even put a bottle of "Lestoil" in it as an old time tranny guy suggested(I had my doubts,but did it anyway!--by this time I nearly lost my job from being late every day because of this tranny!--and I no longer cared if it finished it off!)....nothing changed!
I eventually bought everything to convert it to an SM465,and never had that problem again!--I did go thru 3 -12" clutches the first month before I got one with a good pressure plate--2 of the "3 fingered" ones failed in less than 3 weeks!--ended up with a diaphram type....drove it 6 years without any trouble after that...never did an "autopsy" on the TH350--some guy wanted it,so I gave it to him--its probably still in his plow truck doing the same thing!
