Timing belts are 60,000km or 4 years, whichever comes first. Looks like yours is due now. Vibration sounds like it is a balance issue, and I would suspect the Chinese? brand front tyres. Michelin PS4 are recommended by many (including me).
Try Sport mode, it may satisfy your desire for increased exhaust note.
As for a local (non-dealer) service specialist, especially for timing belts, I have had experience with Manta at Richmond. They are very good, but may be pricey. Many have used Eurogarage, but I visited them and there were over-run with crappy non-runners outside which concerned me about parking scratches etc. The timing belts on my Trophy-R are due, so I'm investigating all options.
I've had the same issue with intermittent start/stop but didn't worry too much about it.