Im probably the most knowledgeable non SFI turbo buick guy here.
AJ (dr. frankestein) on the beforeblack section on turbobuick.com is really good with them, I think he was down to the 10's with his setup in a Luv but he is rarely on anymore.
Have you checked this site out?
http://beforeblack.net/
Do Everything cleanup related here.
http://beforeblack.net/tnotes.htm
Step 1- Check your timing. Do you have the factory spark retard box? It may be pulling timing if you have 87 in it and not running right.
Step 2- What shape are you plugs and wires in? I run NGK UR5's. THey are good, mine likes it.
3-Get a boost gauge if you dont have one. Don't trust the turbo lights, it should make 5-7psi or so. If it doesnt look into the wastegate but see if its making boost while driving at cruising speed.
4- Does it run bad from a 50mph roll? Don't worry about brake boosting it yet, get it running well driving around. Cruise from 50 and
5-Carb stuff. Is the filter replaced? Are the secondaries opening? The coughing from idle sounds like a fuel air or spark issue. If the spark is good and secondaries are opening its fuel related (probably)
6- Power enrichment control valve (PECV). Mine never worked right. Its job is to fuel the carb to the air density post turbo. Mine runs way lean with it connected. It will be a port below the fuel inlet. Disconnect the vac line from the carb and plug it. The rubber diaphram inside, it sits right in the middle of the intake, will crumble and back feed/suck fuel and air alternatively between the carb and intake.
I hate to see a carbturbo car cut apart from people asking for help and not getting it so get that stuff done and report back.
🙂