Accounting for Invoices in Foreign Currency

That's one invoice, you seem to have lost the other.

For the purpose of your cost of goods calculation, it doesn't matter when you actually pay, since the payments are just movements in the bank and supplier accounts. You should enter the full invoice amount into your purchases account for the current year.

Use your best guess estimate.

Just guess. You could just use double the August payment (assuming the October one will be the same), or you could try predicting the October exchange rate on the basis of what it's been doing between August and September.

Not quite. What you need is the average of August and October, but you need to "know" it in September. You could just use the September rate. In any case, chances are your guess will be wrong. Probably not by much, but you will most likely have to make a correcting entry in the purchases account for next year, to fix the error.

On the other hand, you don't have to finalise the year-end accounts on day one of the next year. So why not wait until the second payment has gone through, when you'll know the exact Sterling equivalent. Then either slip the correcting transaction into the old year's accounts (if you've already put a guess into your accounts because you sensibly chose to keep your interim accounts fully up to date and if you operate a no-amendments policy), or else just take advantage of hindsight to make the original entry 100% accurate "guess" (if you haven't entered anything yet, or are happy to amend the guessed entry).

For cost of sales, you enter the invoice at the rate applicable on the date of the invoice. You would make an adjustment to exchange rate gain/loss at the end of the year, and again when you actually pay it.