It's standard height 70 cm IKEA table [...] I'm about 5'10" if I did the conversion right [178 cm] [...]
For a saddle chair to be optimal, it should be so that your legs reach the ground without stretching or bending much, in my case around 70 cm. Of course it doesn't have to, but you lose it's major advantage if you don't.
Okay, I just set my desk to be 70cm tall, with a standard 1990s keyboard on top of it. I took a regular wooden chair, ~43 cm tall, and put the HumanTool Balance Seat on top, including its stiff foam pad, combined height from the floor to the middle of the seat is about 56 cm (the back end of the Balance Seat is slightly higher). This is exactly the right height for a chair to be to use with this desk.
It’s slightly lower than I would prefer in a saddle chair, but I’m 6'2" (188 cm) tall. For me, the ideal saddle chair height is more like 66 cm, and the ideal desk to go with that height chair is about 80 cm.
I think for someone about 5'7" (170 cm), the 70 cm desk plus 56 cm seat would be just about perfect, but it still works reasonably well for me. Saddle seats have a broader range of acceptable seat heights than standard office chairs.
A 70 cm tall desk is in my opinion somewhat higher than ideal for use with a standard ~40–48 cm chair (or for those kneeling chairs), unless you have some kind of under-desk keyboard tray. If you’re stuck with that desk height, and you get a kneeling chair, I recommend either getting an under-desk tray, or, if that is impossible, aggressively tilting your keyboard using feet at the back or possibly an extra book or two piled under the far end.
To elaborate: Try to type with your back straight and upright, your shoulders relaxed, and your upper arms hanging loosely at your sides, and bring the keyboard in close enough to your torso so that you don’t have your elbows held far forward or sticking out to the sides. With your hands in a relaxed position, your wrists in as straight and neutral a position as you can manage, and your fingers lightly resting on the middle row of the keyboard, make a note of the direction of your forearms. Tilt the keyboard so that it is approximately parallel with your forearms. With the 70cm desk and relatively low chair, this will probably be tilted upward somewhat, with your elbows bent at a 75–80° angle. You shouldn’t need any armrest, wristrest, or palmrest, at least not while actively typing. If you get an under-desk tray or a taller chair, you can bend your elbows at more like a 90° angle, and lay the keyboard flat.
To reduce strain further, a split, aggressively tented keyboard is a big help. Much easier to adjust to a comfortable position.
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FWIW, I really like certain models of those Salli chairs. If I were the only person using the chair, I think one of those could be a good option for me. We found that none of them was easily adjustable to comfortable positions for both me and my wife (I am about 11 inches taller than she is), compared to the Capisco chair, which is very fast and easy to adjust to a wide range of positions.