Are you serious? This is how it works? I don't own TG-6, but this is why I hate compact point and shoot cameras (and I do own a Canon S-110). They are full of lies, lies, lies!
I'm not sure that the zoom workaround works, though. If you go from, let's say, an equivalent 50mm focal length to 100 mm, you will need to pretty much double the distance between you and the subject so that the subject takes up the same space in the frame (same FOV). It depends on how the camera allows you to change the f-stop along with the focal length, but I assume it is somewhat linearly related. If (you were using a full frame DSLR and) you go from 50 mm f/2, shooting something at a 2 m distance, your DOF is going to be about 12 cm. If you go out to 100 mm f/4 and back up to 4 m, you also double your DOF to 24 cm, but you lose a ton of light. You've closed down your aperture by 2 stops, so even in the best of conditions, you are down 75% of your light. Then, you are now twice as far away from your subject, which means that, without slowing your shutter, you need and additional 4 times as much natural light (law of inverse squares) or 16 times as much flash power - from the flash to the subject and back again means you are now 4 times farther away and the law of inverse squares applies the whole way.
Then again, if it is your only option, I guess you have to buy an R6 and housing work with what you have.