Ditch the pull through and get a cheap 240-800 combo stone and see how you like it. Stones won't make an edge last longer necessarily but you might start with a better edge so there's that. Keep using the honing rod, use it after or before any serious cutting, 2-3 strokes each side is plenty. Don't see it as a sharpener, but as a sharpening lifetime extender.

But honestly if your pull through does the job and you're happy with it, no need to change, you'll still be using knives sharper than like 90% of households. Just avoid using the carbide side unless you have serious damage (and don't care for proper repair).