How powerful of a soldering iron do I need for this job
An approach which often works well for problems of this sort is to have a helper hold a hot air tool (or perhaps less ideally a heat gun) aimed at the work area while you use an iron to do the actual soldering.  

Ideally this would be someone who has used the hot air before, or you can demo a bit with just that, show the role distance plays, etc.  And hopefully you can achieve verbal coordination in having them move it away (and that they know how to safely set it down)

Also melt some solder on to the iron tip to improve heat transfer.