just thought I'd add my idea... Although I'm self learned - so don't trust me.

I've been playing fretted instruments for many years and I'm quite sure I am always making pitch adjustments by bending the strings or changing the amount of pressure exerted by the fingers. Bending doesn't work so well with double courses, (two stings played at once like a mandolin or 12 string guitar etc) because each string bends a bit differently I think.

I certainly try to control the pitch with a clarinet by changing the shape of my mouth. I don't do it very well.

It's obvious you have full control on the fiddle. But if you had frets I think you still would have some control. But I think you would only be able to increase the pitch - by bending string or pressing harder with the bow or pushing down harder with your finger. So I reckon you would want the fret at the lowest pitch you might want for a given note (range). Then you could make your adjustments to get the exact pitch you're after.

At the end of the day you're still going to need your ears, but I'm all for trying to do things differently. It will be a different instrument and playing style to the more common fiddle for sure. I'd love to hear how it sounds.