That's a very old post, but there are no satisfying answers so...
I think your best option is Amoonguss. Regenerator + black sludge make nature madeness useless, it doesn't care much about taunt, and force it out with sludge bomb or giga drain, which can chip the switch in a bit. You can adapt the spread according to what your team need. (Keep in mind that hidden power fire + some defensive investment allow it to switch in and beat SD kartana, which is really useful since it's one of the biggest threats to stall)
Other regenerators users are less reliable to deal with tapu fini, but are also usable, but you need to adapt their moveset: toxapex need poison jab to deal with tapu fini tho (Gunk shot can get pp stalled by a smart player), and reuniclus should use something like tbolt to hit it super effectively. If you don't want to use poison jab on pex, you could use knock off to cripple Fini at least, since a Fini without leftovers vs a stall team is a dead fini.
You can also use mons able to outspeed tapu fini (aim to outspeed the 263 benchmark.) and deal with it both defensively and offensively. Pressure zapdos with 16 EV in speed and a timid nature creep the said benchmark by one point, and can switch in fini easily. If he switches into nature madness, he can roost before the taunt. If fini spams nature madness, it's going to lose the PP war, thanks to pressure.
Pressuring tapu fini with an hazard setter able to beat it can also work, but that kind of strategies are more suited for more "offensive" variants of stall, that aim to win by stacking a big amount of residual damages.
Also, I don't think fini can do anything to shedinja.