The OP wrote they use a Huber screen. Huber often uses bars that are hydraulically optimized bars with a profile like the left one in the picture:
These have a slight funnel effect, so if d = 7mm, a particle with ~8mm size in one direction can get stuck in the part between the rounded tips. I suggest talking to Huber if you can replace the bars with a different form, the wedge shape on the right. This removes the funnel. I have not seen the hydraulic coefficients for these wedges, but according to the what I'Ve read the downstream end is the biggest influence on flow resistance of the bar so the wedges could be okay too. I don't know how constrained you are hydraulically.
I would also check the rakes: It should be so that one rake clears every other space (say space 1, 3, 5), alternating with the following rake (which cleans 2, 4 ,6 ...) so the bars can bend slightly. Also if the rake gets stuck, it should reverse and to try to dislodge the blockage. All of this is, AFAIK, standard with every rake manufactuer and certainly Huber so it should be implemented on your site.
I beleive a modification to the screens should be the first thing to try, because - like you - I don't see a viable alternative. You can have a screen upstream, but then you might as well replace the screens you have. You can try to sediment the large particles, but then you build a second grit separator. I beleive cyclones to be too energy intensive for a wastewater stream and maybe not robust enough for unscreened wastewater - screen waste is mostly tissues (at least where I am), I could imagine those blocking a cyclone or its pump.
The other idea I might consider would be to have a calm, low flow channel upstream of the screen to separate large grit <7mm - maybe just two wide channel with a small weir at the end, to be cleared by with a Bobcat every year or so. Not knowing the site and hydraulic conditions, I don't know if this is viable.