A single-currency close is arithmetic. A multi-currency close is arithmetic plus a set of judgement calls about which rate applied when, and those judgement calls are where months get lost.
This is the process we settled on after several painful closes, written down so it does not live in one person's head.
Fix your rate policy before you need it
Decide, in writing, which rate you use for what. Transactions are recorded at the rate that actually applied to them. Balances are revalued at the closing rate on the last day of the period. Averages are for reporting, never for recording.
Write down your source for the closing rate and use the same source every month. Changing source mid-year makes your year-on-year comparisons meaningless.
Reconcile per currency, never in aggregate
Take each currency separately. Opening balance, plus receipts, less payments, equals closing balance, all in that currency with no conversion anywhere. If that does not tie out, the problem is a missing or duplicated transaction, and converting it to your reporting currency will only hide it.
Only once every currency ties out in its own terms do you convert anything.
Separate real gains from paper ones
A realised gain happens when you actually converted. An unrealised gain is the change in value of a balance you are still holding. These are different things and mixing them makes your margin look like it moves with the currency market.
Post them to separate accounts. Your operating result should be readable without currency noise on top of it.
Automate the parts that never vary
Pulling transactions, applying the rate policy, and producing a per-currency statement are all mechanical. If your provider has an API, this is a scheduled job rather than a person exporting spreadsheets.
What is left for a human is the judgement: unusual items, disputed payments, and anything that did not reconcile. That is the work worth having a qualified person do.