Re-cutting old checkering can really eat up checkering tools/heads.
The old dirt & grit packed down in there and even sometimes what was used as a stock finish grain filler is just what you need to dull a nice sharp tool edge.

Most any checkering tool is expensive now and some nearly impossible to find.

'I find the Carbide single line tools are great for recutting old work. They can do the bulk of the recutting/deepening and working through all that old crud and finish that simply wears
out a nice new tool steel head very quickly.
Then to complete the job, go over it with regular spacer tools to finish it up and bring everything into nice straight alignment.

The Carbine single line tools will last a long long time. A good investment if you are going to be doing the work for a while.
I'm still using a couple I bought in the mid 90's. One is starting to feel just a little dull now.

The GunLine style checkering heads are nice as you can actually sharpen them once they get dull and get some more useful life out of them
If you sharpen them across the face of each tooth, they respond nicely. You can resharpen them quite a number of times that way.
You need a very thin diamond file to do the sharpening.
If you sharpen up and down the full side of the V on each side it will also sharpen the head, but not as efficiently as across the face of each tooth IMO.
Also you start to loose the geometry of the V shape as you take away material in each sharpening.
Not too bad with a single point cutter. But you start to mess up LPI sharpening a multi line cutter or a spacer in that manner.