Rumor has it tight bond III is no good on ipe.
That's just nonsense. Titebond 3 works fine on any wood, including ipé, and bamboo.
I don't really like mahogany myself. As a core I'm sure it will work, but there are better woods.
Since you have quite a limited thickness, only 1/4", you'll need a core of sufficient thickness, preferably tapered. Depending on design, I'd make the core roughly 4 mm (handle) to 3 mm (tip) thick.