Yes, ideally you should create your own thread for your own specific question. However, it's here already so I'll answer what I can. Others will likely be able to provide further detail.
I find the exact opposite - that is, Brewer's Friend is always more accurate to my final data than Bru'n Water. I've put the same info into both calculators, and my measured numbers are usually dead-on accurate when comparing to Brewer's Friend. I've noticed Bru'n misses the mark high every time. I've since gone exclusively to Brewer's Friend. But many people still use Bru'n with desirable results.
Also, you keep mentioning 5.2 for the mash, but that has been proven to not be accurate for measuring. The only mash pH you need to concern yourself with is the reference pH (that is, of the room temp sample you measured). That should be in the 5.4 - 5.6 range depending on style. I'd say you want to aim for the lower end for a Pilsner.
All that said, yes your mash pH will be higher than expected since you are doing such a thin mash. Brewer's Friend does indeed account for this. I input your data into the calculator and got an expected pH of 5.7. This is partially because you're adding slaked lime to the mash, with raises the pH. You should remove this addition from the mash and add it once you begin to boil, since it's only being used for mineral content. Doing that, you only need to up the acid malt to 2.4oz (which is 3.2%) and the pH dropped to 5.41. This sounds like it would work for you. Here's a link:
http://www.brewersfriend.com/mash-chemistry-and-brewing-water-calculator/?id=ZWQQ41X