No, it's not a glycerin soap and I wouldn't try melting it.
What I would suggest trying is another soap brand -- the last pucks from Trumper's were a disaster for me. Been lathering soaps for decades and I figured I could lather just about any soap, no problem. Thought I was invincible. Cheap soaps, Williams, Mitchell's, Godrej, etc. Then I bought the reformulation of GFT sandalwood and I was nowhere fast, lather dries up before you can set down your brush and reach for your razor. Pretty high cost, too.