It appears you have a classic case of cartridge/tonearm mismatch. Everything you're reporting (except the induced hum from the hex wrench, and that will never be an issue when using the cart). The Zephyr is a fairly low compliance (stiff) cart at 10 uM/mN. Your SME is a low-mass tonearm (~6.5 to 9.5 grams) when you do the math, your combination has a resonance frequency somewhere betwween 18-20Hz. It should be about 10Hz. The Shure V15-III has a compliance of 30 uM/mN and in your SME that yields a resonant frequency right at 10 Hz - just about perfect. Here's the reference link: http://www.analogue-classics.com/html/sme_3009___3012.html
The solutions are either increase the effective mass of the tonearm by about 20 Grams (a big wad of florists putty?), Or find a compatible tonearm, or find a more compliant cartridge. You also might see if you an swap your Zephyr for an Aida High Compliance - they're the same price, but as the name implies the Aida High compliance is intended for low mass tonearms. It is also a high-output cart, so no MC preamp is required - just a regular MM phono stage. https://www.sound-smith.com/cartridge-compliancearm-mass-chart
Good luck.