I stumbled across some additional data, while searching for priority1 ...can't remember where.
It was suggested a larger coil could do what I wanted, and Robert suggested
In you're case you'll be looking at a 30-35 cm coil.
I'm thinking about 50 turns, with 0.25mm wire. Just add or remove turns until the coil resonates at 134khz. You'll want the coil voltage to be sitting at about 300v peak to peak.
His other coil details are here RFID coil antenna
You seem to be on the right track, and I suspect you will have more luck with the ID-2, as I have read they are very good.
Some other details I found here wethepeoplewillnotbechipped.com which use a ferrite rod.
Let me know how you get on m(dot)beckett(at)amuri(dot)net
Thanks
Mark