FYI bellower PL is only for chanter skills and does not syneeguze with wizard. I tried to do a bloodmage bellower and no deal guess 3 PL was too powerful for some mage spells.
Also I agree the next best choice is tactician bloodmage. You proc brilliant a lot and cover for the main downside of a caster even more than bloodmage, which is lack of spells in long fights (the recharge rate is actually pretty damn fast, you could spam minolettas and dd spells like there's not tomorrow). Not to mention the discipline proc as there are some nice melee choices you can work with too (citzals spirit lance).
Bloodmage is actually the weaker of the two imo (since brilliant does kind of negate the whole sacrifice buff when it procs) but a nice way to get a 1 PL bump vs picking the other wizard subclass choices and getting locked out of certain schools.
Just...never get flanked