Am I correct that a 6503 Ultegra FD will fit either a clamp or braze mount? You can just remove the clamp fitting and it will fit a braze mount, right?

If it's a true clamp type,that's it, no removal.If it's a braze on mounted on an ADAPTER clamp,then it can be removed and used on a braze on tab.

The 2 types exist, i.e. there is a config that's band-mount,and one that's braze-mount. The latter can be band-mounted with an adapter. See https://bike.shimano.com/product_imag...00&6503_EV.pdf for a more visual answer to your question.