Been there - symptoms identical. The speedo shuts off when the battery volts are too low.
Regulator is shorted I presume - it is a finned assembly located vertically on the rear subframe under the passenger seat. I believe you may be confusing that with the ECM which is mounted on the front of the battery box.
The smoke is most likely coming from the wires from stator to rectifier/regulator. There is good chance that the stator will also be cooked as it is (likely) supplying current into dead-shorted regulator. Unfortunate effect is that if the rect/reg fails it often takes the stator with it. You may also have to replace the sub-harness between the stator & regulator if the cable is fried. (if it's a 2002 model, there was actually a recall on the original harness which is laced into the main harness assembly - the recall supplied an auxiliary harness of thicker gauge wires)
I'd be most surprised if the ECM is bad but again, I think you have a case of mistaken identity regarding the ECM vs. the Regulator/Rectifier.
These parts are VERY expensive from OEM - try
http://www.ricksmotorsportelectrics.com/
If you have an ohm meter you can check the rectifier/regulator assembly - unplug both connectors of the rect/reg from the harness then check in turn between each of the three yellow wires in the three pin plug to the red, then the black of the 4 pin plug (the two reds & two blacks will purposely already be connected together anyway so pick either one for test). If any of the yellow wires reads short to either red or black, then your regulator is toast - it's not repairable. Also check from the red to black - that should not read short either.
Here's a reference thread for you -
http://www.triumphrat.net/daytona-de...-heatsink.html
See the note in post #3 regarding the harness cable recall. You can buy that part separately if it wasn't already done or you can lobby your dealer to give it to you if you provide the VIN.
Note that my regulator/rectfier is in a slightly different position from yours - mine is custom mounted because it's on an early model subframe, part of custom swap. But the actual part is still an '02+ part so that should help identify your rectifier/regulator for you. Pull your stator cover & inspect the stator - I would expect it to be burned too.
