340 Engine issues

You still didn't say what the lifters are hyd, or solid. you say lifters are adjustable? what does that mean?
Runs great cold after 30 miles it starts shaking, this tells me that the exhaust valves are growing and now are being held open by the lash being to tight. If they are solid lifters. If they are hyd and the push rods are to long? It wont be balance, it would do it all the time, timing? I doubt it.