I also do not have experience with the older sizes, so maybe Nigel or somebody else (Dave, Bill, George,...) will want to chime in?
I assumed that if you get two tyres of a similar make (material, width, cross section), one in xx-630 and one in xx-622. If those two xx numbers are the same (width) then the total diameter of the wheel + tyre will be 8mm bigger for the xx-630 one. Thus my suggestion to go with something more road bike like (21-23 mm width). If you want a softer ride, you might be able to use a slightly wider rim with the tyre you now have. This will "flatten" the cross section of the inflated tyre slightly. It might just be enough to work.
Then, looking at the figure, it seems as if the 27" really means the outer diameter. This would then be smaller than 28" (which would be comparable to the 700c or ETRTO 622). This would mean that my hypothesis (similar cross section at similar width) would be wrong.
Let me use a quote from a Tarantino flick: "Standards. Do you know them, M*F*?". How many yards was a chain again and how many chains to the furlong? But I disgress / despair...
To be honest: I'd stick with the "weird" brake setup
it is working... but on the other hand you might want to make this bike ready for L'Eroica...