Thanks for all of the input. I have just opened an ANA Mileage Club account as (according to the posts above) they require the lowest amount of miles and don't charge too much in taxes and/or surcharges.

Unfortunately, the ANA website doesn't let you search for Star Alliance partner award availability unless you have a certain number of miles in your account, so it's over to ExpertFlyer I go…

My plan is to seach for availability on ExpertFlyer (for a few different dates), then call ANA to confirm the availability, then transfer the miles from AmEx. Hopefully that will be a winning formula…?