157 mV measured across the TPS with the throttle completely closed...
Yeah, I know, that doesn't help much.
If you are only just starting in on working on the bike yourself, I would suggest looking at these three threads first. I only bought my 2002 V11 Le Mans about 18 months ago, and found them very helpful in quickly getting to a point where I can start to do sensible work on the bike (which needed it, and still needs a bit more...).
read that one first, then look at these
A tip for getting the tank off: your 2003 V11 should have the "click-on" connectors for the fuel lines. Be careful there: the plastic elbow coming out of the tank is fragile, and about as easy to find as hen's teeth. What helps a lot: pull the plug on the fuel pump, start the bike and let it run until the motor dies. This relieves the pressure in the fuel line, and makes it possible to disconnect as easy as it is possible to get it. To disconnect, push the connector firmly towards the tank, pull the ring back and pull the connector off.
PS: mine coughs too. Pretty much as you describe yours. Going through the "decent tune up" helped quite a lot. Further research remains to be done...