I don't think the boards need to be ballasted, or heavy enough to sink. That would be true with a centreboard that needs to sink under its own weight, but you can use one tackle to push the board down and another to pull it up. When you release the "down" tackle, if the board is not under load, then it will come up easily. I've seen them pop up on their own! But usually they need a little tug. With the lever arm provided by a 5:1 tackle, and the directional effect of the case - the pressure from the tackle can only go in one direction, either up or down - the boards should go up and down easily.
Especially if you put the windward board down just before you tack, when it will have minimal load on it, then haul up the board that was previously to leeward after the tack is complete. If you were willing to cant the boards inboard at the top by 15 - 20 degrees - whatever the optimal heel of the vessel to windward in 15-20 knots of wind - then the leeward board would be vertical, and you could leave both boards down when short-tacking as the windward board would be canted out at 30-40 degrees and would be providing some righting moment, if it was doing anything. The top of the cases would take up a bit more space, of course, but you could always stow your wine bottles behind them!
If the boards are built from appropriate structural closed cell foam, with splines, rather like a surfboard, maybe even 6mm thick carbon fibre splines, with some exotics in the epoxy layup, it will be massively strong.
I'm not saying this is the only way to do it, just the way I would. I might even be wrong, since my daggerboard experience has all been on multihulls. Even though these boards are going on a monohull, though, it is a small boat and the boards are proportionately small as well.
Annie, you said you wanted some lively debate about the Sib Lim challenge, and you are getting it!
PS: (just added this) Ballasted leeboards may well be the easiest solution here, which can be raised and lowered effortlessly from the cockpit with a single tackle on each board. I sailed with this set up on Grace Ellen in 2014 and was impressed. If the hinge pins and their brackets are strong enough, they are structurally very robust. My experience of daggerboards is that you may well have to step up onto the deck at times to "encourage" them to go up or down, due to pressure on the boards in the case. Since the boat is moving, there will always be some pressure, and no amount of ballast will overcome this.