I too have two full grown (80 ft) Sycamore and a full grown Soft Maple in my front yard. The Sycamores are the biggest problem. .... with stix galore after every routine storm. I can't think of a thing, nor even imagine something that will collect the branches and stix that they drop year around.
I bought a Cyclone Rake a few years ago. It is great for leaves and such things as pine needles, pine cones...maybe even a walnut or two....but, mowing over the stix, just cuts them up without sucking them up. Likewise, my Pine Needle Rake is good for Pine Needles etc....and somewhat effective at general debris in rough areas.....but of no use in gathering Sycamore stix/limbs.
Your idea about stabilizing the Pine Needle Rake tines sounds like it's worth a try. In the meantime.....I just "pick up' or hand "rake up" the crap every now and then.....and then haul it off to a burn pile or run it thru my
Chipper Shredder.[
Cheers,
Mike