"Normal vertebrate development mechanisms" don't seem to allow much by the way of bone reduction. Bones get bigger, or they get porous, or they break (autotomy suggests an option, but I don't think that counts as a fish rather than an amputated frog). *Note that tadpoles lack not just bone in their tails, but even cartilage, apart from elements that remain in the adult frog. (cite)
I would go with a different sort of 'metamorphosis'. You have a species of direct-developing frogs that somehow retains the plasticity to produce a fish-like form under some circumstances (compare the evolution of axolotls ... nothing I can cite will be very exact, and making it a precise copy of a lobe-finned fish tests the reader's credulity). The frogs are capable of a very resource-intensive pregnancy with just one egg, which is favored in this case. The egg hatches internally, yielding the fish form, which then proceeds to eat its way out of the mother, exiting by the mouth, then consumes the remainder of the carcass.