You got a badge? Wow! You've really got the Audax bug seriously! You'll be counting points and putting in for awards next!
Tyres: important things for speed, comfort, grip and simply carrying on. Having had a blow out on my second 200 (tyre delaminated inside and out – up to that point it had been incredibly reliable and virtually puncture free) I'd say speed is not the most important of these, unless you're racing of course.
Ask yourself: are you a speed monster? Would you become one if a carbon-fibre Pinarello (insert brand of choice) fell from the sky into your hands? Would you actually want to be or care? My guess is no you're not and you probably wouldn't be. Were you pushing the time limit on the Tasty Cheddar? No, you weren't. Would you like to be able to ride so fast you could stop for a pint in every town you pass through on a longer audax? Just don't do this even if you can, okay!
In other words, I'd stick with what you've got until you feel a reason to change it.