I was just on my way out when I answered the first part of this question so now I'll do this part (with the reminder that I'm not anywhere near a pcb expert 
). First Fritzing doesn't appear to create a mill layer gerber (at least not anything that says that or looks like it could be it in the gerber directory) so I suspect that needs something like eagle or kicad and thus likely isn't an option for Fritzing. That said both the data sheets listed show the pin as being 3mm by 1mm and given that the only Fritzing option seems to be a hole, then as they say the pth option (which creates three 3mm or 0.118000in holes) seems like the best option and should fit any of the listed jacks. I expect that's why they say that PTH is the best and most tested footprint option in the description. While it will have 2mm of space on the 1mm side of the pin, I expect (without having a board to try it in though) that it should be tight on the 3mm side of the pin and any less won't fit. If you have access to a 3mm drill, I'd try and drill 3 3mm holes in a piece of fr4 and try the connector in them and see how well it fits.
Edit: followed my own advise a generic 2.5 mm barrel jack like the Jameco one with 3mm by 1mm slot, a piece of fr4 .1 pad per hole board and a 3mm drill bit in the drill press. Two 3mm holes at .25in apart and a third 3mm hole mid way between the first hole offset by .2in (the third pin on my jack is only 2.5mm not 3) and the jack fits fine. There is a little spare room but not overly much and I've drilled out the plating so a plated through hole would be tighter. Looks to me like the PHT foot print is as they say, the correct one to use. As a bonus (as mine are like the Jameco one with solder tabs) there is enough room to put a resistor wire through the tab on the bottom of the board to give it additional mechanical strength if you like.
Peter