OK. That works. You can only have one form per Post Type. That is why we have the setting on the General Settings tab Choose which kinds of pages S&F will try to do this on
and you correctly ticked Tag, Category & Taxonomy Archives
.
On the Display Results tab there is also Enable filtering on Taxonomy Archives
in the Template Options
and you have ticked this also, so you should not need 3 forms. You should be able to use the same form on each.
Note that the taxonomy/taxonomies that form(s) the page URL (in your case tool_type
, goal
and region
) also has to be (a) field(s) in the form for the plugin to be able to auto set it/them (you can hide the field(s) using custom css if you need to, often per page, if the body tag has a unique class you can use).