The old fiddle I inherited from my grandfather is gloriously loud but the E string could etch glass. Currently on whatever was on it when it came out of the loft (vintage 1987, at a guess).
Before I spend a fortune experimenting: what are folk using for a warmer top end that still rings for the Shetland stuff? Dominants? Something else?
Dominants with a plain gut-feel E like the Goldbrokat medium is the classic budget answer. If it's still shrill after that, it's the fiddle, and the answer is to sit further from Davie.
I heard that. But yes — new strings first, then get the soundpost checked before blaming the instrument. A millimetre of soundpost movement did more for my tone than thirty years of practice.