I'm no brewing pro, but I might have a few things to add to these tips as just "food for thought". The squeezing the bottle trick, my wife and kids do that when we buy pop and they kind of introduced me to this idea. Now when it comes to brewing root beer, it may not be a bad idea but I would think that it might be possible that once it ferments for so long the bottle may not tighten up or could take much longer to get to that point. I also was told that the amount of carbonation is based on how much yeast is put into the batch. I don't know if this is true or not, but if it is then I would also wonder again, will the bottle tighten up if this squeeze method is used? If it doesn't doesn't tighten up, will you know when its done fermenting?s
If you are wanting to check for CO2 leakage you could submerge the bottles in water and see if you get any bubbles. You could even, ever so lightly, squeeze the bottle just to see if you can push a bubble or twos worth of bubbles from the bottle. If you get no bubbles than its all good. Also, keep in mind that if your bottles are upside down, the sediment in the bottles will settle down to your cap rather than the bottom of the bottle. This may cause you t get a mouth full of that stuff when you open it to partake of the first sip. If you were really wanting to leave the bottles upside down, a few hours before enjoying your brew, I would shake them up just a little to break the sediment up then tip them upright so that the sediment settles to the bottom of the bottles.
Like I said, I'm not brewing pro, just kind of thinking this through and hopping it might help you in finding something that will work for you. Good luck and let us know how it all goes.