Banking: I need a commercial bank that can cash USD checks, pay local salaries, and wire funds abroad. Does it matter if both banks share the same global brand (e.g., Citi, HSBC), or can they differ?

This would come under the purview of Transaction Banking, almost any bank that has a good retail and business setup would be able to do this for you. What the bank will see is how much it can charge you for the transactions or balance that charge with the amount of money you deposit with them.

Its a balance of # of transactions, transaction charge, cash-at-valut (which banks hate) and short-term/long-term deposit average.

What you are asking is something very normal. Your best bet is to call the transaction banking group and ask for a solution/proposal. Compare all the proposals you receive and work the numbers, for example on an Excel spreadsheet work out what 3-months of transactions will cost you - you can even ask them to do it for you.