Then all me to ask this for sake of discussion: which non-tallow based soaps have you tried until now?
All of the Trumpers offerings except for Coconut. Taylors Sandalwood, Truefitt & Hill Luxury Shaving Soap, Floris, Gold-Dachs Spezial/Rivivage, Van Der Hagen (both the glycerine and the tan-colored soap), Col Conk's (Amber, Lime), Valobra Almond soft soap brick, couple of the various Sues, and a couple of the Classic soaps. And the ghastly Proraso soft soap. May have forgotten one or two more - after awhile they all blur together.
Tallow soaps I've used include MWF, Penhaligons (all), D. R. Harris (all but Marlborough), Valobra almond shave stick, AoS (all), Tabac, Williams. I don't know if Marvy is tallow based, but it sucks anyway.
I've been doing this long enough that I've gone though whole pucks of several of these, so my opinion isn't based on a "shaved once and didn't like it" kind of experience. But anyway, I like a variety of tallow and veggie hard soaps, but have yet to find a glycerine soap I enjoy shaving with. My favorite soaps are pre-reformulation Penhaligon Blenheim Bouquet (tallow), Gold-Dachs Spezial/Rivivage (veggie), Trumpers Limes (veggie), and Harris Arlington (tallow). AoS and Valobra tallow-based soaps aren't bad but perform too much like a cream for my tastes.