Couple of new datapoints

PMI - often lots of bikes, might be worth booking this route. But there are at least plenty of flights per day. Very easy at baggage reclaim and check in; they are very used to bikes.

BRI - came out speedily through a door next to reclaim. Bit of a walk to car rental. Check in very easy, no issues.

Qatar Airways - seem good; bike included in checked allowance as long as under 300cm total (for routes other than Africa/S America I think, where is 159cm so basically impossible).

Oman Air - thought I’d give them a go now they are OneWorld; make a big song and dance on the homepage about sporting equipment being included, turns out in buried small print that bikes have to be 159cm total dimensions, so impossible with a bag. If you go over this, you have to pay the “large special baggage” fee which I thought would be about £100 as with most airlines. No. It’s $720. Per flight. Completely mental. So I cancelled the ticket.