What's the reasoning behind lowest profile head depth? I've never found the head thickness to be a major issue in any properly designed razor. For that matter, open combs can be very mild razors, despite reputations for being aggressive. Most thin headed "vintage" razors are open comb. And that was one of the exclusions.
Also, research on vintage razors was easier 10 years ago. There was less information then, but much less SOTD posts cluttering up the search results.
My particular interest in this hobby is non-Gillette DE razor design prior to the modern era, and the more creative the design, the more interesting it is to me. The tiniest variation can completely alter the way a razor shaves.
I think you are excluding many very good razors due to the number of exclusions and wants, some of which don't actually matter to the shave or face feel.
If you asked for a handful of vintage razors that offered mild shaves from Gillette or other brands, without all the other stipulations, you would have gotten pretty much the same answers you have here. If you want to dabble in vintage, Gillette's are the easiest to find, and usually cheapest, depending on the model. A three piece Tech, a flare tip superspeed, a New long comb, and a Slim Adjustable will give you a nice selection of some of Gillette's milder old razors, with the new long comb being the most aggressive of the three non-adjustable razors.
Another reason for mentioning the Cooper MonoBilt was that it was brass, but thickly chrome plated. Most MonoBilt razors still look pretty new, despite being 90 years old. If you are super fussy about "used" razors, the Tech will be the easiest and cheapest to find NOS (new old stock). The other razors I mentioned of Gillette's can also be found NOS, but those are far rarer, and thus more expensive. Replated and/or refurbished razors are more expensive than just finding one and sending it to be plated.
The best place to find vintage razors is eBay. If you bid instead of BIN (buy it now), use Gixen or some other ebay sniper program. Plug in the max you are willing to pay, and the program will insert your bid in the final seconds of the auction. Keeps you from spending more than you are willing to, and keeps other people from nickel and diming your high bid into oblivion. You are literally throwing money away if you don't use one.
The best place to find vintage European razors is Etsy. Just search for "Bohin razor" or "Leresche razor", and check the sellers until you find the ones who specialize in wet shaving. There's a few, and they are easy to find if you know how to look.
To get you an easy start on Gillette razors, there aren't actually that many different types of Gillette heads on razors, so it is possible to "collect them all" if you go down that particular rabbit hole. Between U.S. Gillette and U.K. Gillette, there's probably about 50-100 distinct razor head profiles over the course of 100 years. Most of those are very similar to each other and can be grouped together. All in all, about 30 razors will cover every major advance Gillette made between 1920-1980 on two continents. (As long as you don't start chasing really rare razors)
If anyone hasn't mentioned this to you yet, the British and U.S. Gillette companies might as well have been seperate companies. The razors range from near identical to very different, depending on the model. Where the models are nearly identical, the British razor will be the better made of the two, but a tad bit more aggressive, due to the usually heavier weight of the razor.
It's really less of a rabbit hole than a sucking black hole. I've barely scratched the surface here.
For a basic, but thorough overview of the various Gillette razors:
https://www.google.com/search?q=raz...mcast-us-revc&sourceid=chrome-mobile&ie=UTF-8
He is one of the few people who have a encyclopedic knowledge of Gillette razors, and the only one of those I know of with a youtube channel.
Have fun!
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