Hi Dave,
Sorry to hear about your issues.

I'm not an expert but here is what I would try on a "normal engine"
(when I state normal I mean not governed/controlled by a sealed magic
black box)
When you say "bog-down" I would read that as "engine not effectively
burning the mixture and creating any power" perhaps further description
would help a little?

Does the car belch black smoke when it bogs? - does it spit back through
the air filter?
Does it missfire and feel like a "soft rev limiter" that you can drive
through? does it "pink" or knock?(sometimes sensed as a tinny light
rattle sound) or does it just accelerate smoothly - but too slow for
your liking?

A rolling road could be a good place to go and have it diagnosed (though
will not be a cheap DIY thing)

It could be any of the below - and perhaps even a combination..

too much fuel going in or not enough fuel going in (running rich or lean)
OR
the right ammount of fuel going in but the flame front starting too soon
 or not starting soon enough (too far advanced or retarded ignition)

Drive it till it bogs and then stop by cutting the ignition rather than
driving through the bit where it runs sweet (do this somewhere quiet and
safe !!!)

Take the spark plugs out - what colour are they? are they evenly coloured?
This will not tell the mixture as such - it will only tell you if the
plugs are a suitable heat range for the mixture you are presenting it with
but as a rough guide if you have replaced the plugs with ones that BMW
have suggested as suitable heat range it will give some indication...

black/sooty or worse wet with fuel? - running rich - throw spark plugs
away if they have got wet with fuel - they NEVER work the same
afterwards no matter what you do to clean/dry them out

white or glazed or worse chipped/melted - too lean - though you would
ususaly get some backfire through carbs/throttle bodies if this was the case

If the mixture is up the spout - perhaps the lambda sensor is buggered?-
that /may/ make sense if it runs ok from cold and as soon as it goes
into closed loop from the O2 sensor it richens up to the point of
bogging (your plugs should give a clue here and be back/sooty)
but then again not being a BMW brain surgeon I would not put money on it
running this way

Not sure if injectors can "stick" - perhaps when they get hot they are
getting jammy somehow? - a second hand (known good ones) would probably
be cheaper than having yours cleaned and checked

Get a manifold made - and stick a set of motorcycle carbs or twin 45's
on there and regain control of the fuelling ;-)
OK perhaps not as I don't think having them sticking out of the bonnet
would look as "in keeping with the BMW way"

For the ignition timing
get a stroboscopic timing light attached to a HT lead and put a mark on
the crank wheel somewhere
fire the car up (from cold and have a look at how far the ignition
advances at several RPMs) - you say that when it is warmed up it does
the bog down thing - so check that it is still advancing the same amount
once warmed up

Could it be that the BMW brain advances the igntion till it senses knock
 then pulls it back? - perhaps the knock sensor is not 100% happy?
(again not a BMW brain surgeon so am taking wild stabs in the dark as to
how they control timing advance)

If not, I'm not sure what you can do about it other than clean all contacts
- Trigger wheel/VR sensor on the crank/knock sensor etc) / replace the
"brain" that controls it
(or rip the ignition side of stuff out and go for MegaJolt and have 100%
control over what its doing..LOL)

Hopefully in amongst my ramblings there may be some stuff to chew on
that may help in some way

Regards
Rob

Hi, with all the stuff you already check/change, only 3 things come to my
mind...

1- Have you check the fuel pressure regulator... The symptom you talk about
look like the engine is missing fuel on acceleration.
2- funny thing could happen with a faulty cam or crank sensor
3- the vibration-damper at the front of the crankshaft. Check if the rubber
between the pulley and the teethed gear is cracked.
  even if you can't see crack(s), it would be a good idea to visually
check, with a timing lamp, (like Rob suggest) what is happening
  when that fault occur. I don't remember that kind of problem on 4 cyl.
engine but I do remember a couple times on 6 cyl. engine.
  With a cold engine the rubber is hard and strong enough to retain is
proper position. After a couple minutes the rubber get
  "softer" and stretch a bit, just enough the change the reading of the
crank sensor and feed the dme with a wrong crank speed.
  Sometimes it "wobbles" just enough to miss a reading as well (quite
rarely). That's all I can help, good luck and let us know.

Sylvain