Don't post a lot (obviously), but learn a ton from you guys.
I've used AHS Mozz kit a bunch, and early on experienced similar results. After taking a look at http://www.cheesemaking.com/howtomakemozzarellacheese.html
and doing some reading, I think the AHS formula was very slightly overaccidifying my milk. First, I got rid of the CaCl2 as many recipes don't call for it. Then, I backed the acid down to 1 and 3/8 tsp in trial and error over several batches. The result was a really tight curd formation and really stretchy, moist mozz. Might be worth a quick try before seeking out more milk--my milk was really similar to your description.
As an agricultural product (especially sourced locally) our milk varies just like the hops, malt, and water from area to area. Given that, the formulas aren't exact, and it seems like cheese folks fiddle with it at the margins a good bit.
In answer to the question, I've never measured the pH, but absolutely will the next time around.
I just made my first batch of mozz today. It didn’t work out exactly as expected but the end result is awesome anyways. I can't get raw milk here, but I did get some non-homogenized whole milk from a local dairy.
I got a kit from Austin Homebrew Supply. For 1 gallon it was 2 tsp of citric acid and 1/2 tsp of CaCl2, and 1/2 tab of rennet. I'm other sure if I over-stirred after adding the rennet, or if something was up with the milk, but the curd sank to the bottom instead of floating and was in really small bits. I was able to fish most of it out with a small strainer. Once I got it in the microwave it set up fine and I was able to stretch it and get it into a nice ball.