Strategic Shift:

Play: During Strategy phase before first card is picked.

Does: Choose one strategy card. No player may choose that card this round.

Can you use this on Initiative? There's nothing in the rulebook or errata that says you can't, but it effectively allows the current speaker to get first pick twice in a row - just by using an action card. It also forces someone else to pick last twice in a row; quite a large disadvantage.

Additionally, if you take the rules literally, the speaker is free to choose Initiative again following this (theoretically, if they had 'Synchronicity' as well, they could do the same thing again).

It happened in our first game, so we may be interpreting the rules incorrectly; but if not, it just seems a bit broken.

I think you're interpreting the rules correctly, but I also think the Action Deck is big enough that this won't be an issue most of the time.  It's one card in an already ridiculously huge pile.

If it really bugs you, though, I don't think a house rule that it can't be used on Initiative would be out of line.