Mine is an Avantgarde on standard suspension, 16" wheels. And I'd say mine is firm, bordering on harsh. So I'd probably find yours horrendous.
Not sure what the Conti tyres are like, but mine came on Bridgetone Turanza ER30's - 205/55R16 on the front and 225/50R16 on the rear. Bridgestones are noted for stiff sidewalls and they felt like iron rings rather than rubber tyres! I put Michelin Primacy HP's on the rear as soon as possible but it didn't make a significant difference. However eventually the fronts wore out and replacing those with HPs made a bid difference to the ride - it's a lot more compliant, and quieter too.
Having said all that the lower profile of your tyres mitigates against finding much improvement with better riding tyres.