"Can't you ever do something right the first time?" If I looked more closely at photos, perhaps … I noticed that
Churchill had bogies with "short" bolts on the underside, which is normal for relatively early ones, so I cut them down on the kit parts. Before on the left, after on the right:
And then I noticed something else:
Churchill also had early roadwheel arms, without holes in them for the bolts that hold the rubbing plates on top of the arms — on M3 mediums and early Shermans, those were attached by screws through the top rather than with bolts from underneath, as they were later on, OK, so how to solve that? One option is to cut away the bolts and putty the holes closed, but is a lot of work because it's all in a hard to reach spot.
I then recalled that I have a full set of bogies from a Takom M3 mediums, which someone gave me because the whole undercarriage of the
Vargas M2A1 medium resembles nothing from reality. And because the M2A1's wheels were narrower than those of the M3, I won't need the wheel arms for that once I get round to building it. And what do you know? The Takom arms fit the Asuka bogies, although you need to shorten the axle pins slightly because the holes for them are slightly less deep in the Takom parts.
On the left a Takom wheel arm, in the middle one with the central rod cut away, because
Churchill didn't have those: if it had, there would have been a bolt head visible on the outside, and those aren't in the photos of
Churchill except on the spare wheel — compare them to see what I mean. On the right, both sides of the wheel arm with a wheel glued between them. The wheel is from MiniArt because it's better than the Takom ones:
Left to right Takom, Asuka, Miniart, Dragon and Italeri. The holes in the Takom wheels are clearly too small, if you ask me, and the sides of the tyre are vertical instead of sloping inward slightly. Vertical sides are correct for early wheels, but I don't think
Churchill had those.
Before and after:
Happily, I only glue the wheel arms into place on Shermans once the bogies are on the tank

The only snag is that I couldn't keep the wheels as revolving here, because MiniArt's are a fraction wider than Takom's, because of which the inner arm didn't quite reach the axle. Only by glueing the three parts together do they stay in position as they should.
All together now:
And in the spirit of "Also show your mistakes": the bogie at top right. I had cut the axle down too far by accident, allowing the wheel arm to just slip out. By drilling a hole in the bogie and enlarging that in the bogie, I could just a bit of plastic rod in as a replacement axle. I do still need to cut it down because the bogie doesn't fit against the hull like this.