Utilizing the sheilding is part of killing the interferance between you and the NID.
Keep in mind part of the problem with DSL is that certain things that send out or leak a radio type frequency, and will interfere. Like a 900Mhz phone or even having the modem right under the monitor or TV that leaks.
You migh be able to get away with Cat3 but that wasnt tested and the regular wiring or that type of thing your trying to replace. Plus Cat3 won't give the copper your looking for.
The only thing you might do or try is a thicker style of two wire. that might equil the Cat5 twisted. But that will still be prone to radio noise again. In other words doing it twice.
Just a note:
here's a message from someone that did it the way its shown.
yeah, i actually took the pics and the instructions and wired up my neighbor's NID. Increased his speed by at least 15%. I haven't been able to get out and do mine yet (cursed weather) hopefully this weekend tho. The diagrams helped for my old NID.
inside_attbi
15% over what he was getting .. ? If your getting the 85% of your circuit now, that gets you to 100% If all goes well and it might cost you about what you pay for one months service the most on a one time install.