EXCUSE ME? Sakuya has time stop, Youmu has slowdown, Reisen has phasing bullets, Orin has reviving zombie fairies, Futo has a boat, Seija has screenflips. The only gimmicky stage 4 bosses are Seiga with reviving Yoshika and maybe Murasa with her anchors. Changing spellcards or different bosses depending on the character/shottype is not a gimmick in and of itself.
Like I said, just because those spell cards are unique compared to other bosses in their respective games doesn't necessary make them gimmicks. Stage 4 bosses having the gimmick I mentioned has been around since Touhou 4. That's a more notable gimmick than the so-called gimmicks of stage 5 bosses.
Aya and Minamitsu are the only stage 4 bosses with no gimmicks.
On the side note, this is the plot according to Reddit: