I'd cut them on my 6" bandsaw, same way I cut the firewood loads for my locos. Yes, I know that's not what you want to hear......
Woodworkers as a breed are much more common than railway modellers, so I'd think there would be at least one friendly one in your vicinity. Do you have anything in the UK like the Aust. 'Men's Shed' movement?
The only way I can think of making what you want is to cut strips from balsa sheet, which is easier to work by hand than harder woods like pine. Distress the edges a bit, run a bead of glue along the edge and dip it in suitably coloured scenery flock. It won't stand close scrutiny, but once stacked under a roof, it won't be that visible anyway. Also the 'bark' won't fall off over time the way real bark tends to do.
I know you'd prefer not to go that way, but given that the UK was importing 90% of it's timber before WW1, most sawmills would have been resawing baulks of imported softwoods rather than milling locally grown trees in the period you model. It would still need to be railed in and taken out the same way.
Regards,
Graeme