I see the radio you've got now. Don't try to modify it. It will just wreck the radio.
The problem is AM antennas, by their nature, are directional. You could partially solve the problem by making sure the radio is oriented on its side, which would make the loopstick orient up and down, and that might help ease the directionality a little.
Or get a radio that has a little more pull, which may naturally would be a little bigger. The maker or your radio has a few small portables that you could still stuff in a coat pocket (or in between your coat and your shirt) that might have more sensitivity and you'd have less problems with directivity.
Tecsun also makes a few very small portables that might have better AM band performance than your radio.