How long can i run this engine without the shroud before overheating to check for intake leaks.

Thank you, no leaks found do you have an idea of what i should check next.

with so many unknowns, you may decide to invest in shop manual for that vanguard...

I think shop manuals are available for free online. If you can hold the throttle shaft back and it idles down- then the issue is with the governor or set up linkage. If by physically manipulating the throttle you change nothing, then you have a throttle plate issue.

Thank you
for your input it is appreciated. I have been using B&S manual
272144 to isolate 1 problem at a time on a Briggs 385777-0349-E1.

I am able to lock the throttle shaft in
place and maintain engine speed 2800 rpm and above it runs well the
lowest it will run is between 2000 to 2200 cycling and sounding
terrible(exhaust noise).

The throttle plate and throttle shaft
are connected and operating properly. I don't understand how it can
run so fast with the throttle plate slightly open. The carburetor is
a #844371 if that is any help.

Well, you should be able to keep it running at a lower RPM- which does indicate a carburetor issue. But there is obviously a governor issue as well. So much for stating the obvious! So, have you done the static governor adjustment? Or any cleaning of the carb itself? It does seem like the linkage may be in a wrong hole. Post a pic if you want. Maybe you could clarify what you mean about the terrible exhaust noise. Popping through the exhaust maybe?

Troubleshooting multiple problems that
all interact is as bad as finding an intermittent one. Static
governor adjustment done by me, carb done before DW got it, probably
just opened and sprayed. Governor linkage seemed to be correct
according to every diagram I could find, all of the tangs looked to
have been adjusted.

Tractor is in excellent shape, engine
has 120# compression each side and the wife wants it so I believe its
worth fixing.

The carburetor will be
disassembled and cleaned. The only other thing that worries me was
the engine being run with #1 cylinder rocker arm pivots installed
wrong bending push rods and holding the valves open.

"The only other thing that worries me was the engine being run with #1 cylinder rocker arm pivots installed wrong bending push rods and holding the valves open. " That does seem rather bothersome, having a hard time visualizing this though. Look closely at the valve guides and see if they protrude from the head similarly. it might think it is an Intek...

In regards to the pivots they were not
seated into the detentes of the rocker arms but crosswise to them
forcing the rockers in an extra ½ inch.

I pulled the engine so it could be
inspected fully, I will know more tonight. I appreciate your help with this,
thank you very much.