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I am seeking recommendations for tuba mutes that most closely approximate the mellow(ish) tone of a string bass (and/or cello) with a clamp on mute attached to the bridge. Thanks.

If you can find a Humes & Berg bucket mute, that'd be my first pick. One of my fellow students (years ago) found one and brought it to our college, and we popped it onto a 20J. Sounded fantastic.

Here it is -- Velvet-Tone is what you'd look for.
https://humesandberg.com/home-page/prod ... horn-mute/