I am sure you know about the pay to work.I believe the minimum retirement age is 57. But you would have to take a reduced retirement if you retire before 62. Your pension is reduced by 5% for every year you are under the age of 62.
You also only get a multiplier of 1.0% rather than 1.1% if you retire before 62.
So example: Your 3 year high salary is $100,000. You retire at 56 with 36 years. First you will have to defer you retirement as you are not old enough at 56 to receive one. So until you are 57 you will not receive any retirement. Since you retired before reaching 62, your multiplier is 1.%. 36 years X 1% for each year of federal service is 36% so you are entitled to 36% of your high three salary (in this hypo $100,000) as your pension, which equals $36,000 per year. However since you are retiring before the age of 62 you have to take a 5% penalty for each year you are younger than 62. That is 5 years, so your pension has a 25% reduction. Your pension in this hypo would be $27,000 per year.
Now second scenario. You wait until you are 62. This gives you 6 additional. You now have 42 years of federal employment. Because you reached 62 before retiring your multiplier is 1.1% rather than 1.0% so 42 X 1.1% = 46.2%. Assuming you have the same $100,000 three high, your pension in this scenario would be $46,200.
So by working for 6 extra years you have increased you annual pension from $27,000 to $46,2000. My advice is not to use an early retirement.
In terms of turning your TSP into an annuity. It depends on how good you are with money. If you are not good at budgeting and are likely to blow through your TSP money then use an annuity. If you are really good at budgeting and can live just off your pension, then maybe keep the money in the TSP.
I will hit that at 56/6mths.