There really isn't that much you can do about it. As mentioned, the big piece is the fuel surcharge line, with second place going to UK- and Australia government fees which you can't avoid unless you start somewhere besides the UK and/or skip Australia. By starting in the UK on an LONEx you're already getting a price which is considerably cheaper than anywhere else in Europe, so reducing the UK taxes by starting someplace else would have a negative outcome.

I doubt AA would be interested in issuing the ticket as you have no AA segments planned. I also don't believe you could book LHR-AMM using the AA code unless the segment was married to an AA metal one.

If you want to "decode" those items listed as "tax description unavailable" you can start the (laborious) task here.