The Tudor bodkin is pretty useless against plate. It was developed as a super-cheap head for piercing textile armour such as a gambeson, and was obviously one of the very last head types created, as gunpowder soon ruined everything.
I don't think the swept broadheads were used at all. I'd chalk that up as artistic license, to look more impressive in paintings. If you were painting a field of archers, by the time you got to the arrowhead and tried accurately portraying a Type 10 bodkin nobody would be able to see it. A massive, cartoon style swallowtail is far better for artwork, and totally impractical on the battlefield, but as they existed as hunting heads I imagine the artists had no qualms about depicting them.
A good solid bodkin or lozenge plate cutter will kill or drop a horse just as easily as a silly broadhead point, plus they actually go through plate. The minute you start giving different heads for different jobs in the same battle, you're getting into Hollywood-style myths.
One head, designed for maximum use in the period is all you need. Otherwise you're either asking each archer to have numerous types (impractical for many reasons) or dividing groups of archers to do specific jobs (also impractical). You're also saying that they are being handed sheaves of huge swept swallowtail-tipped arrows - where are they being stored? You can't use them with arrowbags...