You are not dealing with warped wood here.
Your last picture shows that you have a moisture problem (due to a change in the ambient moisture content of the air - change from a dry climate to a wet climate, moved outdoors from a controlled environment) that has caused the bottom to expand and in the process push the the front legs forward, breaking the end grain to face grain glue joint.
No amount of clamping, screwing or gluing is going to repair this.
There is excess wood and you must remove material.
It looks like there is about 1/8" of excess wood(the width of the crack between the leg and the end panel). A wide saw kerf should do the job, but I don't know how to do this without badly scratching the front skirt, but it will be the back of the skirt and out of sight. Someone else might know of an elegant way to do this in situ.
- Use a hand saw and cut a kerf using the front skirt as a guide. This will badly scratch the skirt, but it will be out of sight.
- Use a so called electric multi saw or a reciprocating saw.
- You might be able to attack the problem from the top side of the bottom pieces using a very thin chisel.
Ultimately I foresee a lot putzing around by the time you have removed sufficient wood, but it should be out of sight
Once you think that your kerf is wide enough use a bar clamp or a pipe clamp to draw the from leg back against the end panels (I suppose your ratchet strap would work as well). If there is still a gap, remove more wood.
Leaving the clamps in place, attach glue blocks (blocks of wood that are glued and or screwed) to both the leg and the panel. Don't plan on gluing the panel to the leg.