i had a similar problem with a os .40 fp (similar to the LA series, has an airbleed carb) it would die on me at about 1/3 throttle and would vibrate badly at idle.
the problems was simply carb adjustments, you have to learn how to tune these airbleed carbs. (my highend was a little to rich and my low end was a tad to lean)
the main needle valve controls all fuel adjustments, this works fine at full throttle but the problem is it floods the carb at a lower throttle setting. thats what the airbleed screw is for, to lean out the mixture.
basic tuneing is as follows, set the airbleed screw halfway into the little hole (you can use a pin or just look at it), then go to WOT and set the high speed needle.
go back to idle and let it sit for 30 seconds, then "floor it" to WOT again. if the engine pauses then revs the mixture is to lean CLOSE (tighten) the airbleed screw some more (in 1/8 increments), let it idle for another 30 seconds then floor it again. if it starts to stumble (sounds like its missing/loaded/or just this gargleing sound) then loosen aka lean the airbleed screw. try this again and again until you floor it and it instantly gains rpm's (a little gargle is acceptable)
now what i have noticed, is i tend to set the highend a little to rich this really messes up the midrange, so i slowly advance the throttle one click at a time (1-2 second pause inbetween), listen to the engine and see if it starts to gargle, if it does lean the high end just a few clicks and see if it goes away. (it should)
since i figured that out i havnt had a deadstick, im useing a pos gms glowplug and either a 12.25x3.75 or 12x4 apc prop