Sighted artist here... I'm not sure if this suggestion will be helpful or obvious, but since nobody else has commented so far I will give it a shot. Have you tried using an embossing stylus with a smaller nib for your tactile drawings? I have not used the Draftsman, but after digging around a little online it looks like the stylus that comes with it is has a nib size roughly the same as a ballpoint pen. Will it make a smaller line if you use a smaller tool? If possible, lines of varying widths might get your more of the detail and depth that you're after.

I recently made a little series of embossed drawings using a five-dollar set of styluses ordered from amazon. There are many options, but here is the link to the set I bought:
https://www.amazon.com/gp/product/B00LQYS1GE/ref=oh_aui_search_detailpage?ie=UTF8&psc=1
It comes with three double-sided styluses: the largest is about the same ballpoint pen size, and the smallest is so tiny that it's practically a needle. It might be worth trying if you haven't before.

I also really enjoy carving drawings out of those rubber and linoleum blocks used for making stamps, but I have sliced my fingers a few times in the process!

I can kind of answer this! Back when I took courses at BLIND Inc in Minneapolis, we had woodshop classes and a tactile drawing technique- you'd take sheets of... I think they were aluminum. It felt cold and smooth but moved like construction paper with that *wub wub* noise. We'd draw into it with a pen or pencil, leaving indents which worked like visual lines. I never got the hang of it, I preferred using power tools so I could work on my projects.

There was a period where I'd etch into braille paper with a skewer. It's probably not all that worth it, given what you've tried and what you're asking for. It was kinda difficult to apply enough force make detectable marks, without tearing the paper, and this made it hard to maintain precision on certain strokes or fine details. I could sorta do the same thing with a paperclip or a thick key, but it was significantly more difficult with those.

Depending on what your vision is like, maybe digital drawing? I used to draw using pencil and paper and right when I was getting (what I consider) okay at it, I had to get a lens transfer. So now my eye (I only have sight in my right eye) struggles a lot with contrast. I don’t draw often now but I have an iPad Pro for when I do. It’s pretty slippery but it gets the job done.