You can go MUCH hotter than that. That's definitely where the problem is. Use a nice big tip on your iron and set the temp at closer to 400 C.
I don't know why some people are so hesitant to turn up the heat on their irons. I always run mine at ~750 F (400 C), and I'll turn it up even hotter when doing big through holes on ground planes. I only turn it down for items that melt easily (connectors with big cheap plastic bits) or that need a lot of solder and it'll take a while to feed it all in anyway, but I never go below ~600 F (315 C).
I agree, look here for the tip temperatures that Metcal irons run at (no adjustment other than changing tip) the 500(obsolete)/600/700 series are 302, 357, or 412 deg C respectively with the default for use on FR4 tips being the 412 deg C ones
http://wsbenelux.nl/wp-content/uploads/2014/11/metcal-tip-temperatures.pdfOr here for the Weller Magnastat tips, 260, 310, 370, 425 deg C (most common I encountered were iirc 370 deg C but it was probably a couple of decades since I last used them)
http://www.farnell.com/datasheets/44151.pdfFor problem holes use lots of new 60 tin 40 lead solder (or preferably Sn62 which has 62% tin, 36% lead and 2% silver) and a flux core, high temperatures,
at least 350 deg C and preferably closer to 400 deg C, a well tinned iron with a suitably sized and shaped bit (I prefer conical for through hole and desoldering, some prefer chisel) Solder sucker available for less than five quid on ebay or desolder braid, or a syringe needle. Get enough solder in the interface between the iron and the joint to effectively heat the joint. If you can get a melt to fill the hole with the new solder then you should be able to get a melt to remove all the excess solder from the hole. Putting an iron on a joint at 300 deg C is a waste of time. If the board is genuinely FR4 and manufactured correctly then you won't damage the laminate or the bond between the copper and the laminate using 400 deg C as a tip temperature even if it takes 20 or 30 seconds to fully desolder the joint
Very occasionally you'll get a boards with holes you will never fully desolder as you'd like, but they are typically the ones with huge flood filled power / ground planes with copper three times the usual thickness or with a damaged via.
Most of my desoldering is with a 30+ year old 45W Weller EC2002D (infinitely adjustable 250 -450 deg C) or a 40W Metcal with a 700 series tip (412 deg C) with a sucker or desolder braid (servisol or chemtronics). I've got a Weller desoldering station with a built in vacuum pump that iirc is 60W but it is very rarely used these days.