I don't personally own a Murph but I'm looking forward to getting a Murph 38mm. I've already been shopping for straps and I don't know why I thought these camo suede straps would go with it https://bulangandsons.com/products/camo-grey-suede-leather-watch-strap
Interesting design, lots of novel things in its spec sheet. I'm concerned with the mixing of metals in the case design, like 316L stainless steel case and Grade 5 Titanium case back. Mixing metals doesn't tend to go very well, and could lend to accelerated corrosion due to galvanic corrosion affects. Could be worth mentioning to the founder of Bohen. Otherwise, looks like an interesting brand and I hope they're successful.
Looks like a cool watch, and super cool that it comes with a Jubilee-style bracelet! Your search for a mechanical movement will be physically restricted to the movement dimensions (diameter, height) in order to fit in the case of the watch you currently have, and I haven't seen too many salmon colored dials with a day-date movement for cheap. But if you have dimensions for the inner diameter of the case, and whether the dial comes through the front of the watch (crystal side) or through the back of the watch (case back side), then those details will also be important. Might be a lot of work to take on though.
If you like this look and don't mind getting something else instead, it will be easier to buy an existing mechanical watch that has a lot of aftermarket support for it, say for example the Orient Kamasu. There are also some popular modded Seikos (search Seiko 'Datejust') that look pretty similar to this,
If it's any consolation, I've had the exact thing happen with my setup as well. If you can find a black cloth (shirts, jackets, tarps) to set up over your camera, I've done that before and its worked really well to mask your camera's reflection
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