For those who need it in the future, found the solution, so now the html report/form can trigger the given tool to run. Turns out the tool_state value wasn't the problem. It was the <input type="hidden" name="input" value="%(dataset_selection_id)s" /> value that was wrong. Solution: the xml tool template that triggers rendering of the html form needs to pass the right dataset id to the form (which then passes it to the target tool) so one needs to have $selection_file.id passed:

<command interpreter="python"> blast_reporting.py $blastxml_file $tabular_file $html_file $out_format $selection_file $selection_file.id $html_template ... </command>