i am an artist who bought a square vintage table with round legs that's VERY wobbly. it sways from side to side in every direction. i was so excited about doing a resin art top on it that i didn't even try to fix it's legs until i was nearly finished with the art resin / mixed media top. i thought i'd be able to just tighten the screws in each leg, but they don't tighten! i've searched the internet looking for a video or instructions on how to stabilize this table and haven't found anything that fits the scenario. i have been contemplating removing the screws and using my mom's old technique of removing the screws and filling the holes with toothpicks and woodworkers glue before putting new screws back in it, but i'm hesitant to try something that might not work. i've attached photos of the table. as you can see, there's a shelf beneath the top that appears to be attached with nothing more than a small "toenailed" nail into each leg. i'm hoping i won't have to completely remove the legs to fix them because i'd also have to remove that shelf to get the legs off. how would you fix this problem?