Would יותר טוב be wrong?
It's ok, should be accepted.
That's what I wrote, and they accepted it.
If they're not accepting it, I would report it if I were you
Isnt שלחן without the עבודה also "desk" (and table)?
In Hebrew שולחן עבודה is a type of שולחן, as its name suggests, so it's not really wrong to refer to a desk as שולחן, just less accurate.
Difference between "צריכים" and "זקוקים"?
There isn't a lot of difference. צריך is much more common, זקוק is more formal.
צריכים את משהו וזקוקים למשהו