if the battery does not have enough power to turn the engine fast enough then it may not want to start. when you go try starting the engine after it cools off it take less effort because the cylinder would have eventually let go of the pressure. also if the alternator is not charging the battery like it sounds like then that could big reason why it is not wanting to start. you should be able to take the positive and negative battery clamps off and your truck should continue to run. i know i have swapped batteries in my truck while it was running. just makes the alternator work a bit harder.
91 & 81 d150 carburated 318's 93 R.C. F.I.318