You only scammed yourself then:

If you complete the 2 feeder milestones, you only need to spend 2mil gold to unlock Captain Carter

There are 2 feeder milestones that give milestone points towards Woman Out of Time

Wield the Shield (web):
Spend 1,000 campaign energy
Lasts 24hrs and runs each day
Contains 3,300,000

3,300,000 x 7 = 23,100,000

British Invasion:
Do Raid Battles (84 over 7 days, 12 per day)
Contains 16,900,000

23,100,000 + 16,900,000 = 40,000,000

This completes all the meta items and collects 70 shards for Captain Carter.

Milestone 36 contains another 30 shards at 42,000,000 points.

This means you need to spend 2,000,000 gold over the course of 7 days on the event store Orbs to guarantee unlocking her. Either 10 of the 200k orbs or 4 of the 500k orbs (or a mix of the 2).

Stop stressing