Maybe there is also more to the service that the OP has yet to explain. As it's stated on the last part, "an account they can send $900" into which they will get back after the completion of the transaction, could they be dealing in some kind of business that they don't want to share details about?
 
I don't get why someone can just decide to send transactions to one another for no reason, wasting the fees that it will cost them for each transaction.

just use a multisig

both sides send a public address to each other
use those addresses to create a 2 of 2 multisig
(if you want 2 multisig addresses(escrows) both sides create 2 public addresses each and share them to create 2 multisigs)


fund the multisig and then when its funded you both have to decide on the destination(s) and amount of the fund(s) which you then both sign for

no middle man needed. just each other being co-signers to make sure it only leaves the multisig when both sides are happy with destination and amount and time to let it be spent

in short you both become your own escrow

If I understood your question correctly, you don't need to use an escrow at all.
You both want to send some coins to a destination, right? Lets say you want to send 1BTC and your partner wants to send 2BTC. So you can easily create a transaction that has an output with the total 3BTC, then include your own input(s) in it with the total being 1BTC and sign each input using the ANYONECANPAY sighash. Then the other party can also sign it using the same sighash while adding their own input(s) with the total being 2BTC.

Keep in mind that the transaction itself remains invalid until the sum of all inputs surpasses the total of 3BTC.

Other details may be needed like what the destination is (one or more addresses) or its type (like using 2-of-2 multisig) and stuff like that which depends on what it is you are trying to do.

Of course, I just don't understand what he wants. If he and his friend trust each other, they can make transactions between them, but the transactions he proposes to make are a bit strange. Using an intermediary, which would have to be a trusted escrow, otherwise there is a risk of losing the money, is usually when there is not enough trust between the two parties.

just use a multisig

both sides send a public address to each other
use those addresses to create a 2 of 2 multisig
(if you want 2 multisig addresses(escrows) both sides create 2 public addresses each and share them to create 2 multisigs)


fund the multisig and then when its funded you both have to decide on the destination(s) and amount of the fund(s) which you then both sign for

no middle man needed. just each other being co-signers to make sure it only leaves the multisig when both sides are happy with destination and amount and time to let it be spent

in short you both become your own escrowYes of course this situation has a history that I didn't explain here. Also before the second transaction happens, the receiving party has to initiate a conversion process. But because it is not relevant for what we have to do,  I didn't mention.

No he's not a friend. There is no mutual trust. I clarified in the original post.

Of course, I just don't understand what he wants. If he and his friend trust each other, they can make transactions between them, but the transactions he proposes to make are a bit strange. Using an intermediary, which would have to be a trusted escrow, otherwise there is a risk of losing the money, is usually when there is not enough trust between the two parties.