You make the length of the business end of the needle protruding from the tip of the iron as short as possible, wrap copper braid around tip+neddle, put on a very small hose clamp on top, then turn on the iron and give the copper braid as much solder as it can absorb.

Then you start soldering, after a few successful ops you figure this is going to be a walk in the park - and are promptly attitude readjusted by a blob of solder dripping off the iron and onto your PCB.

Did succeed in the end, though.