In my view you're doing the calculations correctly, although I have a few thoughts. In particular, good job on not adjusting for inflation in this case and doing the comparisons on a level playing field with 2017 dollars.
However, although 10%-ish is the long-term average for US equities, there is significant variability, particularly over as short a time frame as 8 years. There have been 8 year periods where US equities have lost money, and of course there have been 8 year periods with returns much higher than 10% annually.
The results, then, demonstrate the trade-off. Doing it on your own has a higher average value, but a significant chance of you winding up with less money than the government pension (ball parking it, I'd guess about 40%). Some of these possibilities result in significantly less money (a 0% return over 8 years, for example, would result in a 4% rule of just $3200/year). In contrast, the government pension results in you having a guaranteed good amount, at the cost of giving up some of the upside.
The other trade-off, of course, is inflation adjustment. The 4% rule includes inflation adjustments, but your government pension does not (incidentally, are you positive about that? this could be the biggest factor).
Interestingly, the decision calculus could change depending on when between 55 and 65 you would take the pension. The difference between taking it at 55 and 56 is a 10% increase (55%/50%), which to me would be a no-brainer. In contrast, the difference between taking it at 64 and 65 is much smaller - 100/95 = 5.26% increase.