Ok,.. I have a couple of guesses.
First,.. there's another bunch of spots you can oil that might help. I found one of the machines here with that same mechanism, and it was stiff, maybe not as stiff as yours, but stiff enough my hand's a little sore from all of the playing. (Or that could be partly from the complete dis-assembly of a featherweight today too) Oiling these spots made a difference. It's still not perfect, but it's possible it'll loosen up overnight too.
In the first picture, I've removed the rod and the actuator to show more clearly where I want you to oil. Do both sides of the pin, the side you can see, then the other side that you only see when that metal tab is all the way out. You'll see that the pin moves in and out of the body of the machine, so it needs to be free moving.
In pic number 2, get where that rod starts to disappear into the gear. Again, it's a fairly tight tolerance, and needs some freedom to move.
In Pic 3, the top of the machine, oil all three spots indicated.
Sometimes I oil as I'm actuating, so that I can get the most possible oil in.
Now actuate that puppy a bunch of times from the bottom and see if it starts to loosen up. (watch out for spray if you oiled a little more than needed. I got a bunch of it in the face because I was leaned close to watch.)
Now, take a break and let it seep in and do its work.
Second, the collar on the actuator looks like it's a touch lower than the shaft it rides on. This is about leverage. If that collar is too low, you're working too hard to push the actuator. If it's too high though, the actuator will bind on the metal piece and it won't work properly either. I'd like you to leave this til last though, because I found that adjusting that collar was a real pain in the a.... uhm... rear. The hex screw btw is probably metric. It's not quite a good fit for a 1/16" hex key, it should be a size up, but 5/64 is too big.
Also, I see a shine on the rubber gears above the area we're working on. It would be a really good idea to get that off the gears. Oil / grease will eat the rubber, then you'll have to replace the gears. Not one of Singer's better ideas.