Yep, we must be similar. Slightly shorter arms means that we get gunned down on shirts that are tailored more towards the longer armed spectrum.
MJ Bale shirts for their 37 neck is 64.5cm. This is max 2cm too big in sleeve length for me. The 37cm neck is also too tight, it gives the choking sensation. The 38cm neck is just about right, but that comes in at a hefty 65cm sleeve length. R&B and Herringbone measure from the neck to the end of the sleeve, which I think is completely stupid, so we can't compare those. They would be very similar to MJ Bale sizing.
Having a think about it, HC might be just a smidge short at 62cm, maybe I am a 63, but it will certainly be a very small margin. I am surprised he described his shirts as 'plenty in the sleeves'. I ain't that skinny - 73cm around the waist (belly button). It does mean I usually have to get shirts taken in. However, I don't really like that 'tight chest and waist' look. HC shirts are also the tightest I have seen yet (from measurements provided).
Very smart idea with your Saville Row shirt. IMO, that will definitely be the best option in the long run. We are the same, take the sleeves and pants up, sometimes the fabric at the back. Chest and shoulders are perfect. MTM all the way.