So ignoring IsStandard() for now, I'm looking to construct a transaction with two inputs and a 16-of-20 output, where the 16-of-20 output can be satisfied by any 20 signatories, where none of the 20 are the signatories who sent funds to the input of the transaction.
From what I understand this is possible but want to check this here.
That is possible. The signature limits are per script so in your example only the 16 of 20 is what matters. The transaction could have 300 inputs as long as that doesn't violate some other rules You have to use native multisig because due to the 520 byte redeem script limit the largest redeemable P2SH script will be limited to 15 keys. Make sure you understand the difference between native multisig and P2SH. Sometimes the term multisig is used generically when refering to P2SH scripts. Funds requiring P2SH scripts larger than 520 bytes can not be spent (unless a hard fork is done to raise the signature limit) so you can permanently lose funds.
I am not sure if that is not correct or the wording is just not clear.
There are only signatures for inputs (the whole tx is signed but the inputs determine which and how many signatures).
So you have a 16 of 20 multisig address.
To create the MS address will require 20 PubKeyHashes.
To sign transactions with that MS address will require 16 of the 20 private keys which correspond to the PubKeyHashes.
When "receiving"* funds TO that MS address the only signers are the keys which are required to spend the unspent outputs referenced in the input side of the tx.
When "sending"* funds FROM that MS address the only signers are the 16 of 20 specified in the address.
* I generally hate to use wording like that (there is no sending or receiving just inputs and output) but I wanted to make sure it was clear.
I would highly recommend starting first using testnet due to the potential for losing funds. I would then create some demos on main net funded with token amounts (but above dust limit) before funding with any significant amounts of funds. There are a lot of potential gotcha, the potential for losing funds is far higher than with "normal" transactions. Understand my knowledge (especially regarding P2SH) is incomplete and I may be unaware of something critical. The 520 vs 20 key "incompatibility" caught me off guard (see waxwing post upthread) and that could have resulted in a loss of funds.
You probably should also review this list of limits. https://bitcointalksearch.org/topic/m.6477657 Understand it may not be complete and is a work in progress.
I found this documented demo by Gavin to be helpful (although it is for P2SH not native multisig). Doing it step by step it was the first time for me that it all "clicked".
https://gist.githubusercontent.com/gavinandresen/3966071/raw/TwoOfThree.sh