I have been on STD already for 8 weeks of my 17 weeks being pregnant and am afraid my
pregnancy disability will exceed the 4 months leave allowed by the CA PDL. I've been working > 2 years for a big firm 2000+ nationwide and 100+ in CA, which offers FMLA, STD (3 months) and LTD (after 3 months waiting). While legal, is this common to terminate a pregnant woman on LTD after 4 months on medical leave? In such case, looks like the only course of action for me is to collect the LTD/EDD (my dr supports me) until 2 months after birth (C-section), pay COBRA myself and look for another position when I'm able to work again?

No one here can tell you what your employer may do once your leave entitlement expires. I suggest you speak to your employer as even knowing what others may do doesn't tell you what yours will do.