Here's your problem. Up in the light box, you don't know which of those /3 cables goes to switch box 1 vs switch box 2. So here's what I would do...
... after buying a multi-color 5-pack of electrical tape for about $3 because we are going to color-code everything: neutral=white... always-hot=black... switched-hot=red... travelers=yellow or some other color. There are always 2 travelers in a cable, they do the same thing, they are interchangeable, so code them the same color. "Two marked the same color" is pretty distinctive, as we are usually trying to make wires different colors.
Install 3-way switch #1.
- Start by nutting the two white wires in box #1 to each other. Those are actual-neutral, and need no markings.
- Note the /2 cable (the one without a red wire). That can only be supply. Its black wire goes to the COMMON terminal of the 3-way, this is the one with the black screw. Don't think about position, look at screw color.
- Two wires remain, the red and black from the 3-way. Those will be travelers so tape them both yellow. These go onto the two brass screws on the 3-way.
We are done in this location, so you can reinstall the switch. Next: Figure out which cable is which up-top.
- Cap off all the wires, and go to town with a voltage detector. If you find one cable is hot and the other is not, you are done with this section.
- If you don't have a voltage detector, use the lamp as one. Shut off power, pick one cable and attach the lamp to its white and red wires.
- If the switch makes the lamp turn on and off, you found cable #1.
- If not, try the other cable.
Mark cable #1 and tape the black and red wires both yellow, since they are the other end of those wires you marked earlier. Always mark both ends of a wire the same. It's downhill from here. Turn the power off.
Let's think about the yet-undiscovered wires. There are two ends of /3 cables - one in the lamp box and one in switch #2. These can only be the opposite ends of the same cable.
Most people want their lamps connected to switched-hot, otherwise it defeats the purpose of switches. Switched-hot is red. We'll make the other two travelers. That's black and white. Mark both ends of the black and white wires with yellow tape.
Fit the 3-way in the far box, with both yellow travelers again going to the brass screws, and the common (red wire) going to the black screw. Do the work carefully, and we are done here. You can close up the box.
Back up in the lamp box, nut together as follows:
- a yellow to a yellow (doesn't matter which**)
- the other yellow to the other yellow
- Neutral (the only white, thanks to our remarkings) to lamp neutral (white or sometimes blue)
- Switched-hot (the only red) to lamp's black, red or brown (whichever).
Power up, test, should be done.
** Now if you have OCD, and want "both 3-ways down" to be lamp off like I do, and it isn't that way, then go up in the lamp box and swap yellows. Done.