Can you share the HTML of the page? That should give us a better idea if the HTML table designer is not working as intended or if the HTML of the page contains the layout displayed in the designer.
If the HTML is the cause of the issue, then I would try to interrogate the table manually using 'Select Element'. Then you can interrogate one of the rows and it's child checkbox so that you can iterate through the rows and perform actions on it as needed.
You can do the same for any other table you need, or set the match rules in such a way that you can use clones to get a collection of all the tables.
Please find attached sample solution that is able to select one of the "Clause 1" options based on entered text for search.
It uses interrogation technique described above - instead of defining HTML table structure, match rules for underlying controls are tuned so that "row" control matches several rows and it has child radio button "rb" control.