Nice thread! My personal feeling is that if you're after 'special' then you may have to go older rather than newer. I think a large part of 'special' is the bike's personality, including flaws - and in more recent bikes too many of those have been ironed out.
1098R I think it hits a sweet spot of character ( the old school Ducati traits of trellis frame, dry clutch, thumping vtwin torque, 916 inspired looks ) along with modern ish performance ( as long as you're not concerned about chasing tenths of a second with the very fastest guys at your local circuit )
You could take a look at my 999r Fila Replica - its a tad more than your £20 we can have a discussion? Its advertised on here
No to be a killjoy but I find it odd that you want baffles so you can use it on a track, over loud bikes on the road affect the public's view of motorcyclists in particular and are the driver for these new 'noise cameras'.
For me something special it would be a 749R. This bike is a proper homologation special. Ive got big fast bikes but in my opinion you have more fun on smaller nimble bikes. This is a proper race bike for the road.
The 1098R. Trellis, V-twin, true homologation bike, and won WSBK honors from start to finish of its run be it Bayliss or Checa. And with the 70mm Termis, proper thunder! Last of the full fat V-twins imho as it has a raw delivery of power that remains un-neutered compared to the Panigales with loads of electronic nanny aids like anti-wheelie, anti-skid, anti-kill-yourself, anti-fun!