remember

I checked my calcs and I think its 50%.
I am sorry that I cant understand your calcs

1) Let's calculate your oppenet's EV when he 5bet all in.
EV= (the percents you fold) x (binds's 1.5+your 20+his 9) - (the percents you call) x (his loss)
=(z)x(30.5)+(1-z)x(-31)
When EV=0,we get a ballace frequence:50%

3)3bet\5bet AK\QQ is +EV at least.
It's hard to say clearly that 3bet\5bet AK\QQ is better or just flat them is better.
But if you want a wider 3bet\5bet range,you have to do that with AK\QQ.This make you can add more bluff hands in your 3bet\5bet range.

"Being 3betted" is equal to "someone defend you IP" here.If your oppenents have a optimal strategy,their EV is always plus when they do sth. against you. If their EV is minus by some actions,they'd better do nothing to keep their EV being 0.

However,that your oppenents'EV is plus does not strictly means that your EV is minus beacause of the blinds.

In order to set up optimal strategy,I think we should focous on EV both when we are defended and when we are not.

Trying to do sth. to make your oppenents'EV be minus when they defend you IP is impossible.

1 ) "This means if we fold more than 31/100+20+9+1.50, 24%, he auto profits."
supose z is the ratio we fold.
(z)x(30.5)+(1-z)x(-31)=0
z is about 50% ,not 24%

2)"If they 4bet, they are risking 17 (20- their 3bb raise) to win 20 (their 4bet) + 10.5 (the blinds plus the 3bet) so we need to defend 1-20/30.5, 34% of our 3bet hands to stop them exploiting us."

There 4bet will auto profits when we fold 17/(20 +9+1.5)=56%.We need defend 44%,not 34%

3)"We can only 5bet hands for value that have >50% equity vs their calling range."

hands which have >39.7% equity is value hand, eg AK QQ.

4)"We open a reasonable range of; 66+,ATs+,A5s-A2s,KJs+,QJs,J9s+,T9s,98s,87s,AJo+,KQo
which is 12.5%."

You said "reasonable",without reason.
I think the reason is here:
(the ratio we are not 3betted)x(the net when we are not 3betted)-(the ratio we are 3betted)x( the loss when we are 3beted)
We set up an open range to make sure this figure is the biggest and followe the strategy by your analysis process

If the oppenents 3bet us with narrow enough range (eg,AA) or optimal range,they always profit when they 3bet. If your oppenents are good,you lose more when you defend more.
I think what matters here is:
(the ratio we are not 3betted)x(the net when we are not 3betted)-(the ratio we are 3betted)x( the loss when we are 3beted)
We set up an open range to make sure this figure is the biggest and followed the strategy like Ace said.This is optimal I think.