I would not be comfortable with the amount of weight a sled places right in the middle of the tailgate just as the skis leave the ramp and enter the box. 500# sled plus 200# rider and you are probably around at least 600-700# right on the middle of the tailgate. At least with an atv the load is spread out more.
I believe the dealer told me 350# weight limit for a gmc tailgate. I dont have one but was looking at them and had the same concern.
I would seriously consider a hitch mounted truck bed extender and maybe cut the horizontal tube shorter so the support bar is an inch or so from the edge of your open tailgate. Many of these are only rated for 350# but for $60-100 and I saw one rated for 750# and another around 400#.
A new tailgate, esp the multi one from gmc, is probably $$$$$$.
Harbor freight $60. 350#
Maxx Haul $71 300#
Erickson Big Bed $93 400#
EricksonBB Jr $66 350#
Lund $156 750#
Yakima $229 300# aluminum
Darby $100. Unknown#
Ecotric $100? 750#
Tricam. $? 350#