John... perhaps you should ask the mods if they can change your byline from "Confused about dryer sheets" to "Confused about annuities"
Just kidding.
I highly doubt that Vanguard and Fidelity are the only brokers who will sell a SPIA to a pre-tax/tax-deferred account.
There are two reasons why a 3 year deferred annuity payout is higher than an immediate annuity... first, you are 3 years older so the insurer pays benefits for 3 less years and second, the insurer had been able to invest your premium for 3 years before they begin making payments to you.
For example, on immediateannuities.com a SPIA for a 57 yo male has a 5.70% payout rate, a SPIA for a 60 yo male has a 5.99% payout rate and a 3 year deferred annuity issued to a 57 yo male has a 6.73% payout rate. So of the 1.03% difference, .29% is due to your being 3 years older and .74% is what the insurer is paying you for getting you money 3 years earlier.
If you compare the payout rate for a SPIA at age 60 and a 3 year deferred annuity to a 57 year old you can essentially see the "interest" that the insurer is paying you over the 3 years. Based on payout rates it is about 4%... IOW 5.99% accrued at 4% for 3 years is about 6.73%..... pretty good but not stellar.
Regarding your enthusiasm that there is no way you will come out further ahead with stocks and bonds, I think you are wrong and am concerned that you might be confusing the payout rate with the rate of return. Let's say that at age 60 you buy a $100k SPIA that pays you $500/month (a 6% payout rate). 6% is NOT your rate of return. A portion of that $500/month is a return OF your $100k and the rest is a return ON your $100k. It is almost 17 years before you get $100k of benefits so if you die before you are 77 your return is zero or negative. If you have average mortality and live to 80 then you get benefits equal your $100k plus a 1.9% annual return. Live to 90 and your annual return is 4.4%. Live to 100 and your annual return is 5.3%.
AIG is a fine insurer... as you note the issue that they had had nothing to do with their insurance businesses which were sound and it was the sale of some of those healthy insurers that allowed AIG to payback the bailout plus interest. IMO, AIG is more comparable to The Principal, MetLife and MassMutual... with NYL and Guardian a step up from the others IMO.
As I tried to explain to you before... Vanguard and Fidelity are simply brokers making the sale and getting a commission in return. Most likely after the sale you would deal directly with the insurer.
Finally, if you are hell-bent on buying an annuity then your best bet is to defer taking SS until you are 70. You "pay" a monthly "premium" by forgoing the amount you would have received from 62 to 70 and then you get increased payments for life. For example, if your benefit would be $1,500 at 62 and $2,640 at 70 then if you defer you pay a total of $144,000 (forgo $1,500/month for 8 years) and at age 70 get an extra $1,140/month (a 9.5% payout rate for an inflation adjusted annuity... higher than the 7.7% payout rate for a 70 yo buying a fixed SPIA).