330 is not hot enough. 680F (360C) is a good place to start for ground planes, up to 720F (380C) as needed but dial it back down when you can. Use a big tip since that will have a larger thermal mass and transfers heat much more efficiently.
Even better, get an underboard preheater (Hakko makes a relatively inexpensive one....can't think of the part number just now) and pre-heat the board to 150C (300F) to minimize the temperature differential when soldering up top. It really makes a difference. I used to have the same problems as you (many moons ago!) but with a) right temperature, b) right tip, c) underboard preheat I can make good connections to ground planes in <3 seconds.
If you just kept lashing solder on....you may very well have a cold solder joint, you just can't see it. Solder will quite happily stay firmly seated on a pin, riding on a nice wave of insulating flux thin enough that you can't see it, but thick enough to insulate nicely from the pad!
BTW, those "four-way links" are called a "thermal relief" or "thermal pad". They're actually supposed to help in soldering to the ground plane by minimizing heat loss away from the pad. I don't think they help that much 
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