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My workbench is an old drafting table and only about 1" to 1.25" thick - good enough for bench dogs, but a short holdfast doesn't draw tight (the ones from Woodcraft).

I'm thinking of building up the underneath side, but need an an idea of how thick to make the final dimension. Would 3" be enough (adding a slab of 2x) where I would drill new holes through the two layers?

Thanks.
My just received LN catalog says up to 4" for their holdfast, with a 3/4" dia. bore hole. No minimum specified.

If your drafting table top is sugar pine, and the rest is available, you may find it worth more that way then converted to a work bench.
I would say 3-4" is ideal. I have a 4" thick benchtop and the Gramercy holdfasts I have work great on it.
I believe 2.5" is about the minimum.
The sidewall of the holes should not be overlooked.

My main bench has several dog holes worn smooth, no amount
of persuasion will keep the holdfast tight.

I would suggest that you first drill all your holes, where desired.
Then glue a backing strip along the row and use the top half
as a guide to get the rest of the hole depth.

Somewhere around 2" thick, anyway.

Less than that, and you'll start rounding off the top and bottom
outlets, until it won't grip - like mine.
My bench is 2.5" thick holdfasts work fine.

Your top is definitely too thin the holes will wallow out.
When I bored dog holes in the 1 1/2" thick apron on my bench, I quickly found that they wouldn't hold a holdfast very well. I backed the apron up with a 2X4, bringing the total thickness to 3", so they hold much better now.

So yes, 3" - 4" is a good target. If your bench is too thin, the easiest way is to screw some 2X stock to the underside where you want to bore your holes. Just make sure you mark where you want your holes so you don't accidentally put a screw there.