I actually have had a set of the Kelvin leads shown in the BS407 photo for a few years. Ran into an eBay listing with an impossibly low price ($35) so snapped them up without doing too much research. They are made by Pomona and sold as the "Wide Jaw Kelvin Lead Set". The "Wide Jaw" part is why they are not ideal for typical uses. Their "Kelvin Clip Test Lead Set" is a bit more normal. Either way, the list prices on these are pretty ridiculous.
You can buy quality Kelvin clips and make your own set, but also the cheap ones do work well enough.
I haven't spent too much time below 10uOhms, but I think you'll be surprised at how easy it really is to get good results with even the most basic Kelvin setup. Of course typically the best option is a dedicated fixture, but down from there is two sets of alligator clips, or you can use alligator clips for the force and then use DMM test probes for the sense, and finally you can actually get your tongue at just the right angle and use two sets of DMM test probes and just hold them with your fingers like chopsticks.