The inside guts of the HYD connector on the tractor should slide back and forth freely when the male HYD hose is inserted. I have trouble with my tractor too. I have new male and female connectors too. But I don't use them much so either trash or something gets get between the guts that should allow easy seating.. I keep the dust plugs installed too..
I turn my tractor off and keep inserting the connector back and forth and finally it will seat..
I wouldn't spray anything but oil in there since harsh cleaners might cause the O-ring to swell and be useless. But they are easy to replace and will need it at some point.
I think if I ever replace mine I'll try to find another aftermarket female for the tractor.. For the record my tractor is almost new with less than 275 hours..
EDIT after I saw pics: I'd replace the Teflon washer and o-ring inside the tractor connector. If that doesn't fix it, I'd probably replace them.. They are around $39 each I believe..