I have been practicing my re-checkering on some other type guns but am now ready to start work on a coupler LC projects
Observations: I have a pre 1913 Regular frame, early 1920's regular frame and a 30's Era FW frame, all 12 gauges and all field grades with all at 80% plus checkering still visible
Other than LPI differences in the pre and post 13 models all the checkering seems to be just either lines or flat top. Is this correct and/or the correct terminology?
What special tools and/or processes do you recommend in re-checkering these stocks?
My recommendation would be to look at as many original condition guns as you can. Look very closely and take note. Develop an eye for factory work as opposed to checkering which has been refreshed. If the work has been very well executed it will be increasingly hard to tell. Doing that level of work should be your objective. There were degrees of variation in the checkering. Each grade was not checkered identically. Variations in LPI and style exist. Flat top is more durable so better suited to hard use than fully developed diamonds. You will see it used up to about 20 LPI and more on earlier guns Absolutely uniformity is one hallmark of quality work. Nothing is a more glaring tell of replaced wood or non-factory work than checkering that isn't absolutely identical on both forend and buttstock.
Checkering in a sunny window on an icy morning when it's too cold to be doing anything else can be pleasant work. Have fun!