I have a parting off tool using a 1/2 in x 1/8 in file mounted in a homemade holder similar to the one in Len Mason's book "Using the Small Lathe", although Mason suggested using a worn out hacksaw blade.
Mine is 1.84mm wide at the tip, full 1/2in depth, and through experimenting it has a blade length of about 10mm. I have to use a lot of cutting fluid, ie once the cut starts, keep the cut full, and deliberately force it into the work. Under these conditions it works well, but if the fluid runs out, or the cut slackens off, then chatter can occur. I have not heat treated the file – just used it as it came. I have left the top surface horizontal and used the original safe edge for this purpose. No dig-ins at all.
In respect of pre-HSS days, it is worth remembering that, according to Tubal Cain/T D Walshaw, a properly hardened and tempered carbon steel tool is actually harder than HSS. Also, turning speeds using carbon steel are a lot slower than HSS because of the heat problem. HSS = High Speed Steel.
Regards,
Peter G. Shaw
p.s. I note that you have done the job successfully using the ground down file. Congratulations.