*steve*
"It shows you measuring a 4700uF capacitor on it's 20,000 uF range and reading 425uF on it's digital readout."
This is a 3 1/2 capacitance meter. In the range of 20000uF, the reading is correct-4250uF.
"This cap must be faulty and isn't a good unit to use to compare with your meter."
No, this is a new capacitor.
"Second issue: when set to your 1000uF range on your home built tester, the maximum it can measure is 900uF."
No. It can measure 1000uF. Just that capacitor has a capacitance of 900uF.
"1000uF is the full scale for your voltmeter on the 10V range. It would be better to call it the x100uF range, since the output in volts, if multiplied by 100 is the capacitance in uF."
For this there is a switch 1uFx1000.
"Why not have a higher supply voltage so it can output 10V (even better, 11V or 12V to give it some overhead)?"
The circuit elements are designed to work correctly when powered 9v.
1000uF-50v.