Dunhill is the George Luca$ of the pipe world--I suppose we're lucky they aren't asking for a small return by even just mentioning their name.

I think a Case knife would be perfect, but I wouldn't hesitate at a sale-priced Sav Fitsall (thanks PD, forgot the name)...

...the thing about the Kleen Reem is, you can use it like a Fitsall. I've used a Fitsall before, and if you simply narrow down the Kleen Reem to its narrowest, you can use it in a similar manner. I've never used the Kleen Reem for maintaining a cake, just taking down cake that was terribly uneven or simply too thick, always on estate pipes--to give them a fresh start. I haven't had them skip around or "chatter" in the bowl, and if they simply weren't giving an even cut to the cake in question, I narrowed 'em down and pretended it was a Fitsall--then continued as they intended.

I've used the Senior like you describe. Works pretty well that way and when used to hog out a badly caked bowl who's gonna sweat a little chatter?
The Fitsall is probably safer than the Case but after a tad of practice on a beater the Case is hard to beat. I'd like to glom a Fitsall some day but on my income it ain't gonna happen any time soon. I'd like to get a Pete 05 but it's gonna have to wait too. Oh well, I've got the things I really need. Wants can wait till my ship comes in...meanwhile it's the Case for me.