How do I block cables without flattening them?

Blocking is what makes cables pop, not flatten them, so don't be scared of the water. Wet blocking is basicly the best thing you can do for a plain wool like yours because the fibers relax and settle into whatever shape you lay them in. I've done a bunch of heavily cabled sweaters and the puckering you're describing almost always relaxes on its own once the fabric gets properly soaked. Cables pull in fabric on either side, so some gentle waviness at the cable panel is normal even after blocking, but the rumpled look will smooth way out.

Here's what I do. Soak the sweater in cool water with a little wool wash for a good 20 or 30 minutes so it's saturated all the way through. Squeeze the water out gently, never wring or twist, then roll it up in a couple of dry towels and press down to get most of the moisture out. Lay it flat on something foam or a couple of towels, and shape it to your measurements, not to what it currently looks like.

As for pinning, I use way fewer pins on cables than you'd think. I pin the edges and the key measurements, and along the cables I just use my hands to coax each cable strand into a nice rounded shape and nudge the fabric around it flat. Maybe a pin or two at the widest points of the cable if it's really pulling, but you're right that cranking them wide open kills the puff. You want them looking like cables, not like road maps. The ribbed hem is easy. Just stretch it in line with the body width while it's damp and pin it there, don't pull it wider than the body or you'll train it to flare. Same with the side ribbing, pat it straight and let it dry that way.

Plain non-superwash wool is actually forgiving here, it has more grip and memory than slick superwash, so it tends to hold whatever shape you set. Let it dry fully, a full day at least, before you move it.

One pedantic habit I picked up after ruining a cabled vest years ago: pin thru the purl columns beside the cable, never through the cable crossings themselves, becasue a pin pushed straight through a crossing leaves a little dent in the stitch once it dries. Also take a photo of the sweater laid out dry, with your tape measure in frame, before you wet it, since once everything is soaked and stretchy it is surprisingly easy to convince yourself the chest is fine when it has quietly grown half an inch. I also find the cable panel itself wants measuring from cross to cross, not edge to edge of the panel, or you end up easing the background fabric out to match the width the cables were never meant to fill.

Congrats on finishing, that's the scary part over with. One thing I'd add: when it's soaking wet it'll look way worse than it does now, like a sad droopy rag. Don't panic, that's normal and it comes back once it dries. I made the mistake of poking at mine every hour the first time and basically never let it rest. Now I block mine at night and just walk away till the next evening. Also, since it's plain wool, do a little test patch of the yarn if you've got leftover, some non-superwash dyes bleed on the first soak. Better to find out on a scrap than on cream-colored ribbing.

The thing that changed blocking for me was a cheap salad spinner I found at a thrift store. After the soak I spin the sweater in batches for a few seconds each and it comes out barely damp, no rolling in towels at all, way less water to evaporate so it dries almost twice as fast. Worsted wool handles it fine, I've done it for years and never had anything felt or stretch wierd. Might sound odd but for a big heavy sweater like yours it saves your back from all that pressing down on towels too.