Noiz2
Sound Ninja
Off the cuff I would say that to make much of an improvement you would need a better preamp. It's probably not the capsules but the mic pre circuit that is adding the noise. I found adding a good mic pre made a HUGE difference with low end recorders. About the cheapest available is the MixPre, though you might be able to find some used bargains. However that adds a lot to the overall cost of using external mics. I would find one locally and do a test with the H1, but I suspect that you will hear a significant improvement.