yes I have had that exact experience and the car did run. however the post suggests both manifolds are cool enough to place your hands on them.
If I have miss read it then the fault is more likely as you have described. the float chamber level is misleading if the output side is blocked. In my case it was the filter in the banjo that was blocked whereby there was no flow to maintain proper running. on shutdown the locked in pressure would allow fuel to bleed thru the crud in the filter (Strainer) and fill the bowl.
I read it that the front exhaust manifold is hot but the rear exhaust manifold is not nearly so hot. The 1/8" diameter drilled passage in the bottom of the float bowl could be full of tiny particles of rust that get through the filters in the tank, fuel pump and float bowl inlet banjos. In which case it would run on 3 cylinders, but they would still be balanced, firing evenly, so it might not be obvious to the owner that it was running on 3 and not 6 cylinders.
Low vacuum in the intake manifold sounds like the rear throttle plate is not closed.
yup. Carbs need to come off.
On a positive note - Imagine how impressed Phillip will be with acceleration when the additional three cylinders are up and contributing! 
agree with JonV2…I freak out if a slight burble or miss…and can’t stand to drive with it…back to my garage for a fix…if not sooner roadside. I can’t imagine feeling that a car is running good…if 3 cyls were down. Now if no miss or stumble but power was way off, and you had not experienced full power…maybe. I did experience that when I first got the XK and a teeny single exhaust pipe, was then replace with a large diam, and a Abarth style resonator (no muffler). Hills that had required a downshift to 3rd, now easy in 4th and still accelerating.
Nick
I have tried to run an XK engine where one of two carb pistons are jammed, and it will hardly run,
let alone drive (at all)
in addition, once the engine has been running at idle for more than a couple of minutes,
it is impossible to touch exhaust manifolds
I cannot remember what temp they run at on the infrared…mine also has a thermocouple for greater accuracy, but after driving the vehicle, (as opposed to idling), they get very hot.
edit; I checked mine for a possible engine problem, and temps ranged 250-310C ~400-510F on the braches, the front and rearmost branch lowest, centre ones highest
If the ex manifold is not hot, there cannot be adequate combustion