Would something like this be sufficient?
ANTEX HP100 100W soldering iron
It's overkill, it'll work but you're missing the point and there's a very good chance you'll kill just as many boards, what you need is controlled temperature and thermal mass combined with available power to maintain the temperature.
This is what I use (mine is ancient, it's dated 1980 something I think so it must be an earlier version):
https://www.amazon.com/WTCPT-Temperature-Controlled-Soldering-Station/dp/B00004W463As mentioned earlier, try the largest tip you have, you've got at least one trashed board to practice on now so before you dig out a new board, experiment on that, scrape off the solder resist and try to tin the board.
In my experience (and I know this will provoke all sorts of posts to the contrary) for soldering this sort of connector and board you *never* need more flux than that contained in the solder. Hell, I only *ever* add flux if I'm reworking SMD.
Another board, sitting on top of the reel of solder used and soldered with my Weller, no extra flux and just a No.6 3,2mm tip, the board hasn't even been cleaned: