You'll need something a bit fancier than a standard switch to bail you out of this mess

With standard four-way switches, a mid-loop spur like the one between boxes 2 and 3 would require a /4 cable instead of the /3 you've run. However, a more sophisticated system like the Lutron Maestro can handle this without a hitch: simply replace the switch in box 1 with a MA-S8AM and the rest of the switches with MA-AS'es. These can work with only a line, a load, and a single interconnect wire connecting the accessory switches together, which allows for the mid-loop spur you have to be run with the cable already in the wall.

If there is only 1 set of wiring coming to this fixture use the back stabs (I hate back stabs). If there are more than 1 set pigtail and then use back stabs. This is one of the few places I have used backstab fixtures. I would never use the back stabs to jumper the sets, if the pigtail is used the only power being used is by the fixture itself. I have not had any problems with pigtails and back stabs but using the fixture as the jumper I have seen hundreds of failures. There should be a strip guide on the fixture strip the wire to that length. Push the wire into the round hole . this can normally only be used with 14 awg wire. If no strip gauge strip between 1/2 to 3/4 inch if copper is showing a piece of scrap wire or a small screwdriver can be used in the slot to remove the wire and trim it off and verify that no copper is showing and you should be good to go.