You can bend them back as you're holding the parts in place. Generally, it makes no difference to the final product anyway. The parts are soldered into place, and the leads are bent only after
exiting the holes on the back, not on the device itself where it could cause damage. Just make sure the LEDs are facing the direction you want them; you can use your finger to hold it into place as you solder.
Filling in the parts all at once, and then doing all the soldering at once just makes it a lot easier because then you don't have to put down the soldering iron, fit all the parts into the board, pick up the board, put it in the clamps, solder, and repeat. All those different tasks throw you off your rhythm. You'll use less energy for your soldering iron too and you don't have keep cleaning the tip. I'd estimate that if the boards look like the ones in the photo, fitting the parts shouldn't take more than about 30 seconds, and soldering will probably be 15 seconds if you're in a rhythm.
I would also pick up a board vise so that you can just grab the board + parts, fit it in quickly, solder them, and then move onto the next. I use a Panavise Jr vise head
to hold the boards with a Panavise base
(I use the suction cup version
); however, you can get a standalone version with both head and base
as well. Either set make are good investment in my mind.