Not all fake furs are created equal. I have some rycote wind jammers for lavalier mics. IMO, the fake fur I DIY'd does better. But some of that was the closed cell windtech foam that I was using under the rycotes. Ditching both of those and letting the fake fur float freely seems to be noticeably better IMO. You want the dense, soft, and long haired fake fur IMO. 1"+. I got 1/2" fur and layering it is the only compromise that works for me. But it was the only thing available off the shelf at Hobby Lobby. And I got the last square yard of it. And it has to seal, any crease no matter how small will negate the whole. Having some foam under the fur, it doesn't take a lot, can help to push the fake fur out and prevent said creases
You might try putting part of a womans nylon over the H1 before the fake fur and see if that helps. Otherwise HPF, Low Cut, Bass Roll Off or whatever you want to call it can go a long ways to cut the noise, at a cost. Also bear in mind that a wind screen is only half the battle. If the wind turbulence of the device is great enough, it will shake the device (mics) and get recorded as rumble was well. Which is where the blimp / zeppelin device comes into play. They are a combination shock mount and wind screen. And basically the best isolation that you can get (or make). Part area of calm, part isolation from itself and the rigging.
You might try putting the H1 on a tripod and taking your hands off of it while recording. It could be the 1Hz muscle impulse getting mechanically translated into the gear and ultimately the mics that is what you are perceiving as wind noise. Although in general wind noise is much more substantial IMO. Without a blimp, it's a fairly artful exploration to find what works for you. For me I have 2x layers of fake fur and have to seal up the XLR connectors with electrical tape, plus shock mounts before I start to feel like I'm where I need to be. Oddly taping up the connectors is almost as significant as the fake fur. Plus the shock mounts allow me to touch the mic stand and stuff instead of operating in a strictly hands off configuration. Not quite your configuration/need with the zoom, but food for thought.