When you mention 37 mm tube, I’m assuming that’s the OD, not the bearing cup size. We have some remnants of 1-1/2" x .083"w left over from BB shells. ID is 1.33", or 33.8 mm, just about right to ream to 34 mm. Pretty easy to relieve the OD to save some weight. I can send a piece if you pay shipping.
We’ll soon have relieved 37 mm headtubes on our website. 37 mm in this context refers to the finished ID, for a 37 mm bearing cup. This larger size is to accommodate 1-1/8" x 1-1/4" tapered steerers as well as 1-1/8" straight steerers. Wall thickness at the cup is 2 mm, and 1 mm at the relieved center section. We gave some away as pre-production samples, if you’d like one or two for the cost of shipping, they’re yours. If you are never going to run a tapered steerer, stick with the 1-1/2" tube first mentioned. It’s much easier to source a reamer and headset.
See EC37 Vs EC38 Trial: 1.125 to 1.25 tapered headtubes for some pics and a dimensional drawing.