Why doesn’t the tester trip the GFCI

I take this to mean that there is one main wire that circles the perimeter beneath the floor, and right below each outlet there must be a junction box with a separate wire going up to the receptacle.

This sounds most likely, however, if done to code, junction boxes shouldn't be hidden in inaccessible locations (walls/floors/ceilings that do not have access panels over the box). If there is a floor beneath the floor or an attic above, this is the most likely location of the junction box.

You may be able to find an outlet further upstream which supplies power to the other outlets, but in comparing the price of a combination GFCI/AFCI breaker (~$40) with a single tamper-resistant GFCI outlet GFCI (~$20), I personally wouldn't spend any more time investigating for the additional $20 and would just swap out the breaker.

A plug in electrical tester will show voltage and let you know you have power there, but it will not show amperage. So if you have a loose wire connection or a wire break under the insulation on one of your receptacles that feed the others, you will see voltage, but if you plug a light in or something else that will draw some amperage, the voltage drops due to the amperage draw. If you plug in your plug in voltage tester and then plug a light in to the other socket, you will see that the plug in tester shows no voltage or very little.