I've got a gut feeling that this is the CTS. I know this is well off topic, nothing to do with ElanScan and will probably get move into some backwater to get forgotten, but here goes........
My Polo had become troublesome to start from cold and got worse each day. Spark and fuel seemed fine and the strange thing was that it would crank over for a couple of minutes without so much as a cough before finally struggling to very weak running but quite frequently stalled. After about 30 seconds of lumpy idle however, it picked up and ran fine.
I'd found an OBDII reader similar to
ElanScan but not having an OBDII interface (similar to the
ElanScan interface) I was stuck. Thinking about it logically, I deducted that the CTS had failed by going leaky or presenting a lower resistance than normal to the ECU. This would make the ECU think the engine was warm and would be most apparent at cold temperatures when the CTS resistance was at its highest (see Candles' post on CTS resistance above and is previous post on the formula for parallel resistance: 1/R=1/R1+1/R2). When the engine is cold, it relies on the ECU to enrich the mixture (pulling the choke out Pinky

). I decided that cranking it over and over eventually built up enough fuel that it could eventually struggle into life but still the mixture was too weak for a decent idle until....... the O2 sensor had warmed up sufficiently. As the ECU detected the O2 sensor signal, the car goes into closed loop control and the ECU then adjusted for the lean mix and the car ran fine. Although the CTS was out of specification, it did not throw up a CEL as the CTS signal was still within the expected range
The way I proved it on the Polo was by disconnecting the CTS to make the ECU think the brass monkey's balls were dropping. It immediately sprang into life but the exhaust fumes were a bit black as one might expect. Letting it run for 30s allowed the O2 sensor to come online and I plugged the CTS back in.
An OBDII reader would have highlighted the problem to me immediately as would
ElanScan if this is your problem. The Polo and my S2 have the advantage of having an O2 sensor, but the SE hasn't so a consistently lumpy performance is to be expected.
It might be worth you disconnecting the CTS (read
this to see what you're looking for) to see if you can get it started any better.