A pH of 6.0 is indeed the number at which many TFF members will recommend that you do a large water change and recharge your ammonia (during a fishless cycle.) The assumption is that your tap water has a higher pH of course.
Osian may be right and the "pH Up" product may be an ok way to adjust your bacterial growth water. The assumption there is that whatever minerals/chemicals the product adds will mostly be removed at the final water change before fish, I believe. I have not a shred of doubt the TFF members can tell us what is in that "pH Up" product!
I have the same problem of pH dropping to 6.0 and believe it may have greatly slowed my fishless cycle initially. I eventually figured out that my water is extremely soft, which means it is not "buffered", which means the pH will easily drop when the acidic products of fishless cycling build up.
I'm known for doing things the hard way

, so I got a KH test kit and started adding enough baking soda from the kitchen to bring my KH up to 5, thus buffering my "bacterial growth water" so it will retain my tap pH of 7.5 or so for about a week or more, thus saving on the need for water changes.
Of course, pH is just one thing, and may not be the limiting factor for the growth of those stubborn Nitrogen-Oxidizing-Bacteria!
~~waterdrop~~