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After some further investigation and a few more cardboard mock-ups things were looking up. If I worked to a larger scale than 16mm then it might be possible to achieve what I wanted. The Roundhouse Billy all but matched the length and width of Douglas on the Tallylyn Railway at a scale of 20mm to the foot. The cab was too low but that should be possible to sort out as I would want to build it from a kit.
Kits were purchased and the loco built up without the body but including the radio and all worked well. It was relatively straightforward job to cut the cab insert 15mm strips into the side panels and make up a new front plate. The cab was bit narrow front to back but then so was the one on Douglas before it was modified.
But something else was not quite right but it took a while to realise what it was.