Update:
The short version:
Changed out the old MAP sensor with new. No more 'jerks'.

The long version:
I occasionally get under the hood to try and pinpoint what causes the jerking effect. Based on the feedback received; a failing Bypass Valve would seem suspect and indicative of this kind of "bad behavior". I bought a new BPV but haven't had time to install it.
My original one on the car, seems to have the same amount of resistance as the new one. So I'm holding off on replacing it for now.

The other day I hit the pedal pretty hard 1st gear WOT. The car almost died. The dash lit up like an pinball machine. SES, DSC , TPS and went into severe limp mode. The Mini wouldn't power/drive over 12mph. I pulled off the road and shut down....
Pulled OBD II faults:
P0302 = "Misfire Cylinder 2",
P1237 = "Pressure Sensor Intake manifold before compressor ~ input low",
P0313 = "Misfire Detected With Low Fuel"
and a dreaded;
P5E19 = "CAN data fault from DME/DDE (DSC lamp on as long as error is present)"
DSC or TPS warning light(s) are not illuminated on speedo. OBD II still won't clear this fault code.
Restarted and the Mini drove fine. I just took it easy.

Here is what I've tried to diagnose so far:
_Ziptied the BPV shut - Test drove, driving mildly hard as normal when the jerking occurred (about 3.5 -4.5 K rpms). Didn't take long until the Mini went in to 'limp home mode' with the BPV tied shut.
_Smoke test - Made my own out of a jar, tire air compressor, 2 hoses and burned a piece of denim. Worked great. No leaks in any vacuum lines (small amount of smoke made it's way out of the oil filler cap seal).
_R&R'd the spark plugs and checked coil pack & wires. Perfect. (not surprising they're new).
_R&R'd / cleaned both MAP & TMAP sensors. Both looked super clean (almost new).
*_I don't have access to a gauge to test the fuel pressure at the rail.

A kindly tip from @Oldboy Speedwell on another thread; suggested that he had a similar issue and replaced the TMAP sensor. Which ultimately cured the problem.
I had a new MAP sensor (but not a new TMAP), stored away that I purchased back about a year ago.
Replaced the old MAP with new and... Waddayaknow? - I hit the pedal hard 'til the SC starts singing, with no hesitation and with no abrupt jerking.
There's still a tiny bit of a surge felt at WOT in 3rd & 4th but nothing like before.
I plan on replacing my fuel filter over the holidays. It's NEVER been changed. @84k mi, I think it's way over do.

On a side note: I managed to score a set of low millage Siemens Deka fuel injectors (=JCW 380cc's) from a salvage yard. $30 / all four.
I'll install those early next year along with a new fuel pressure regulator....AND see about getting a tune.

 

Just an update as it may help someone else.
Even though I had planned to R&R the SC intake - I was really reluctant to go through and change out the By Pass Valve with the new one I bought last month.
Luckily, I received and installed a new TMAP sensor just before X-Mas.
My Mini now accelerates like it used to in any gear @WOT. Absolutely no dead spots, surging or hesitation = "jerkin' back & forth".
In addition, The exhaust smells A LOT cleaner/leaner. It used to smell/very rich.
I don't know much about MAP & TMAP sensors. Even though the BPV was cheaper than the sensors - I'm just glad that replacing them solved my issues. I can save my new BPV for when the day actually comes.

 

I had the exact same problem as originally posted, P1237 sputtering at a variety of RPMs and eventual limp mode. My bypass valve was changed two months ago (Detroit Tuned) and I switched both map and teammap sensors out for new ones, but aftermarket ones.

Smoke testing found the vacuum port on bypass valve was cracked, not the Detroit tune valve itself but the tube underneath it. Replace that and p1237 would clear and then come right back. Putting back on the genuine mini map and tmap sensors cleared the code and it drove perfectly.

 

Although frightfully expensive - I agree - Reluctantly ($$), I conceded to purchasing and installing both OEM TMAP & MAP sensors.
It's been almost a year since I first posted this thread. 10K later; not one single re-occurrence. To paraphrase a quote from A Christmas Story..."All is right with the world"