I’m a bassoonist.

Use a bari sax with a small mouthpiece.

When I got to my current position (many years ago) we had no bassoon players. To satisfy having the parts covered, I would use two bari players in the top competing ensemble one would play the bari part and the other would play the bassoon part with the key signature and accidentals fixed. It works great.

You won’t be happy with a euphonium, but a metal straight mute is going to be as close as you can get with that instrument, remember, tone color, timbre is a product of overtones and the distribution of those in the sound. Conical instruments act differently than cylindrical. A brass instrument will not be able to produce what you’re looking for.

I’m happy to have two bassoons in my band this year