I can't really tell much from the spreadsheet but we can look at what's reasonable. I don't know a thing about Fawcett Pearl except that it is a base malt. I don't know a thing about Carastan except that its color is apparently 17 L and that it, therefore, presumably has properties something like other malts of similar color and that whatever the differences are they don't much matter as it is only 5 percent of the grist. Same for white wheat. Thus what happens will be determined mostly by the base malt. Most base malts have a DI mash pH between 5.6 and 5.7 and that is, therefore, where you would expect the mash pH to be with distilled water. Using Crisp Maris Otter as a representative base malt the DI mash pH would be 5.69 without any other malts and typical specialties in the quantities given might pull that down 0.01 pH.
Taking the blended water chemistry listed as written we note that the high calcium level might pull mash pH down 0.11 and the magnesium 0.02 whilst the reported alkalinity would offset about 0.06 of those decreases for a net estimated pH of 5.61. Thus 5.7 isn't an unreasonable estimate for the pH of the mash with 20% tap water, be it hot or cold. OTOH 5.4 isn't really a reasonable estimate for the mash pH even with all distilled water or all distilled water keeping the calcium and magnesium but eliminating the alkalinity and I don't need a spreadsheet to tell me that.
I can't really tell why you get an estimate of 5.4 as the spreadsheet is locked to keep guys like me from being able to see how it works. I can see, from what it displays, that the water is given an acidity of 1.5 mEq/L when in fact its effective acidity is more like 0.5 mEq/L. This suggests an extra mEq/L acidity which would explain an estimated mash pH of 5.4 but I don't see any acidity addition anywhere in what you posted. Perhaps I just missed it. At the same time I see total mash acidity listed as 0.5 when, in fact, the acidity of the mash wrt pH 5.4 is more like 1.4 mEq/L. But then although I do know what acidity is I don't know that it means the same thing here.
Stepping back for a minute we an see that a mash like this is going to have buffering of 30 - 50 mEq/kg•pH and that means to get a swing of pH of ∆pH = 0.3 with 6.8 kg malt you are going to need 0.3*6.8*30 = 61mEq to 0.3*6.8*50 = 102 mEq of alkalinity or acidity. And, as what you observed came only from changing the source of 7 L of water we have to conclude that the change in that water was 61/7 =8.7 to 102/7 = 14.6 mEq/L. That's just not reasonable. At this point the possibilities are
1)Bru'n Water does a terrible job of modeling Fawcett Pearl
2)Fawcet Pearl isn't anything like an ordinary base malt
3)You made an error in your pH reading.
4)Something else I haven't thought of.