Trying to calculate grav in an overly-complicated cider making process.

Okay, folks. It's my first time making cider (long time making beer). and I messed up but fixed it. However, I cannot calculate the gravity now because I was adding stuff, modifying and so on. Please help me figure out if my calculations are correct:

First, I made 3 gallons of cider by adding Camden tabs the day before, then heating to 190F for a bit (sterilization overkill?), then cooling and pitching a pack of Safale US-05

The gravity was 1.045 which my cider-loving friend said was too low--she wanted some strong cider.

So I added 1 lb of sugar (dissolved in some boiled water). I know, in retrospect: what a stupid thing (which I was told by a "soft" cider vendor).

When it had fermented down to a gravity of 0.098, I added another gallon of cider (1.045 grav). It fermented to about 1.003

Determining it to be still too solventy, I added about 2/3 Gallon of tart apple juice (unpasteurized) (grav: 1.048).

now, nearly a year later, the grav is an even 1.000

This is my calculation, based on gravity points of the ingredients to figure out what the OG would have been had I put all of this in at the beginning

Grav of the initial mixture: 1.045 of 3 Gallons
1lb sugar into 3 gallons = 1.045/3 gal = 15 points more.
another gallon at 1.045. Now this divided by 4 gallons = 11.25 pts.
the remaining 2/3 gallons of apple juice, at a grav of 1.048, goes into what is now 4.7 Gallons of cider. That's 1.048/4.7 let's just say an additional 10 points.

So, in total : 1.045+15+11+10 = 1.081 as what the starting grav would have been had I put this all together.

With a FG of 1.000, this means 81 X .131 = 10.6 ABV

Is this in any way an accurate estimate?

I'm sure you're used to using water in heat when you make beer. Neither is typically used in cidermaking.

You're math is a bit off. Look at it this way, you used 4 2/3 gallons of cider. The average gravity is around 1.045. To that you added 1 lb of sugar, which has 45 points of gravity. 45 divided by 4.67 gallons and it should've raised the gravity by about 10 points. 1.045 + 10 points from sugar = OG 1.055. Fermenting to 1.000 gives you approx 7.3% ABV.

Thanks. There I go trying to complicate it. 7.3% makes more sense than 10.5 and explains why my friend could still walk after chugging the 8 oz I gave her to try.