Hi, Lyd! *waves* I agree, sailing downwind means sail trim, boat trim, and rudder feedback are less obvious than beating. Your sails transition from lifting foils to drag bodies, but not all at once. Little-known fact: Even a symmetrical spinnaker is a lifting foil, along its windward edge and maybe 1/3 of its girth. Also along its foot. The rest of it is pure drag.
Likewise the main and jib. Around a broad reach, it becomes difficult to keep flow attached all the way to the leech. But you should still try to keep the front portion of your sails lifting, and that means tweaking attack angle. Watch the tells on your jib and the luff on your main; the main will probably give up the ghost first, because the oval mast section will develop turbulence behind it. That's why they invented rotating masts.
Try shoving your jib leads as far forward as you can. Refresh my memory -- even on the Mk2, the working jib sheets inside the shrouds, true? You could run a second set of sheets to the genoa tracks, or in light air we sometimes hand-fly the jib outside the shrouds from a broad to a deep reach. The farther you can get that clew away from the centerline, the farther back on your jib the airflow will stay attached.
Your apparent wind will seem all over the place as puffs, surfing, and boat speed shift it thru 60 degrees or more. Trim for the average and steer small. Bag out the main (ease outhaul and downhaul), and then vang the boom. Maybe give a tug on your leech line, if you have one. The combination will curl the leech in while keeping max draft on the sail. Our SJ21s have no roach at all on the mainsail, so you don't need to vang too hard to prevent the top from twisting off. By vanging, you can ease the boom out farther without the sail hitting the spreaders -- and as Sailordave says, you want that boom out as far as you can get it, to milk lift as long as possible.
Other interesting quirks of the SJ21 below a beam reach: In light air, get everyone back and induce some heel -- to leeward near a beam reach, to windward DDW (may need a preventer for that.) Remember, this boat is just a big dinghy and wants to be sailed like one.
In following waves, especially swells, get the weight aft to keep the rudder in the water. In middling-to high winds and small waves, sail the boat flat flat flat with the weight centered. I've had ours cooking along a deep reach (~150 TWA) at 7.8kts sustained -- not quite planing, but well above hull speed and with the apparent coming right over the beam. At those speeds, the stern begins to squat like crazy: you'll hear a noise like a sump pump sucking air. That's why you need to move crew weight more forward as boat speed increases. It won't ever break loose entirely, but you'll gain from raising the transom out of hole.
I confess I'd love to try broad reaching with the keel up, but I'm too chicken.