Tips should make a pretty noticeable difference with the Annihilator.
Generally, you should steer away from
foam tips. As you've found, they kill upper-treble which puts the focus on the frequencies under that and, depending on the IEM's treble tuning, can actually make treble sound more 'heavy' and forward. They also result in loss of perceived resolution for the same reasons.
Final E tips, which are narrow-bore, usually have this effect albeit with tightened bass response because they're silicone and fairly rigid.
The
Azla Sedna tips, in general, are tips that will make the Annihilator sound brighter and leaner. This is because they are wide-bore, so they let in more upper-treble and don't enhance bass. The
Sedna Shorts (with the blue stem) are probably the most balanced of the Azla tips and (IMO) sound the best with the Annihilator in terms of the Azla tips.
Tips that I've found that take the edge off are the
Azla Xelastec and
DUNU clear tips (not the candy ones or the S&S, they included these with some other IEMs and you might have to dig for them). Not sure if the DUNU S&S would have the exact same effect; I'd imagine its similar, but those tips tend to work better for shorter nozzles.
The Azla Xelastec definitely have a more linear effect where they lower both the upper-midrange and upper-treble, and that's what I'd probably recommend:
Divinus Velvet tips also work pretty well for taming treble.
Personally, my favorite tips with the Annihilator are the Spinfit W1 (which are stock). But those definitely lean a little brighter.
Hope this helps!