Always start with a compression check. Cold and dry.

Tell us a little more.  When was the last time the engine idled normally?  What work was done to it between then and now?  Like everyone says, stick with simple things.  Check compression, look at the plugs for signs of water, etc .  Does it seem like the engine is dropping a cylinder when you slow it down?  Or, does it just run normally but cut off whne the throttle is lowered?  Are you sure the carb sync linkage is OK?  Perhaps the carb butterfly/throttle linkage is stuck open slightly for some reason.  Keep in mind that the choke linkage opens the throttle slightly when the chokes is activated.  So, of the choke linkage is messed up, the carb butterfly will be held open slightly at low speeds which will cause it to stall out.  Is the carb synced properly to the ignition cam?  Have you messed with that adjustment at all?  If you tried to adjust it while the choke was out, then it will be way out of whack and might be holding the butterfly open.

You might want to invest in those cheap neon inline spark testers.  Remove the cover, install the testers inline to the plugs, then run the engine.  Perhaps you are losing spark to one cylinder at lower speeds.

Finally, and perhaps I should have led with this….  Those throttle indicators on the twist grip are notoriously inaccurate.  Does the engine seem to idle properly while it is at the start position?  Are you judging idle quality based soley on that twist grip indicator?  If so, perhaps there is nothing wrong with the engine at all.  Has someone been messing with the throttle/twist grip/horiztonal/vertical throttle shafts?  If so, perhaps the gears are not lined up properly.  Again, these twist grip throttle indicators are notoriously inaccurate, so please don’t judge idle quality based soley on the twist grip throttle position indicator.

Yeah, 37PSI is real low, I would definitely try a different gage.  You will probably only see 70-85PSI readings, which is normal for these engines.  If low readings are confirmed with a different gage, then you need to pull the cylinder head and have a look.  Perhaps the gasket is blown between the two cylinders.

OK, so the engine is new to you, so you don’t know how it ran before.  You serviced the ignition and carburetor.

The carburetor linkage should just start to open the throttle plate when the hash mark on the cam aligns with the throttle linkage.

So, the engine runs OK at the start position, but at a higher RPM than an idle.  Again, make sure that carburetor throttle plate is closing at idle, and that is not being held open slightly by a messed up choke linkage.  Just because the cam isn’t touching the carb throttle arm does NOT guarantee the throttle plate is closing properly.  I guess the only way to ensure proper throttle plate closure is to remove the carb and have a look at the throttle plate from the back side of the carb.

Again, I would try those inline neon spark testers to make sure you are not losing spark at lower speeds.  Just because parts are new, does not mean they are not defective.

So, first I would confirm the compression readings.  37PSI is too low.

Next, I would check that carburetor to be sure the throttle plate is actually closing at idle speeds.

Finally, I would invest in those inline neon spark testers to make sure you are not losing spark on one/both cylinders at lower speeds.

Again, just cuz parts are new, doesn’t guarantee they are any good.  Perhaps you have a defective spark plug, try some different ones.  Have a look at the plugs, and look for signs of water intrusion as well.