Before addressing the latch, solve the hinge issue. There are some great photos of hood latch differences here, so if you search this forum and compare the images once you get your hood open, you can see if your latch has already been swapped. Here's one photo from Tom Brandl's web site, of a '68 latch.


When the hood is closed on this latch, a metal bar rotates out of the latch body. This will cause issues (not able to open hood at all) if you have a '67 style hood, but if you have the angled hood receiver you should be fine.

Lubricate the hood latch thoroughly with PB Blaster or other penetrating lube. The latch is also adjustable, with three bolts on the latch support, if it still makes contact after opening.

If the latch is not touching the hood after you've released it from the safety, then it's not the main problem. I have to open my '69 hood the same way, and it has all the correct parts. Pull, press, pull, lift.

You can try lubricating all the pivot points on your hinges to see if it helps. Use graphite lube, or PB Blaster, or another very slick, non-drying lube. If your hood sticks almost closed, be patient, just try repeatedly lifting with a gentle lift until it eventually opens.