There's really not a lot to say about which emulator to choose, as all roads lead back to EightyOne by Mike Wynne.
As mentioned in other parts of this site, the only real issue I found with emulation vs. the real thing is with HiRes video. Various online examples of HiRes code work perfectly within an emulator but causes severe video sync problems on a real ZX81
Mike Wynne is something of a giant in the field of Sinclair emulation who pretty much did everything then stepped away from the emulation scene. Simon Holdsworth took some of his work and created a Java and JS version called JtyOne. I received an email from Mike and sadly his depature from the emulator scene was due to health reason. Wishing you well Mike and hope you get back to where you were.
Simon Holdsworth's JavaScript port of Mike Wynne's Java ZX81 emulator
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Try:
LOAD "3DMAZE"