On competitive boats back in those days the thin needlespars would have been stabilised by a spigot. This was a species of mast stump, rigidly fitted into the boat, and projecting up 6 inches or so, onto which the main mast telescoped with as little play as was compatible with being able to get the mast on and off. In the absence of one of those you badly need lowers, otherwise, as described, the mast will just bend up when the weight on the wire takes the load off the spreaders. This is also a sign of inadequate rig tension...
If decent rig tension is inadvisable - shroud ought to have, I reckon, at least 20% more tension than the weight of the crew and the more the better - then in theory you could fit check stays to the base of the spreaders, then the leeward one would tend to stop the mast bending up to windward when the load comes off the windward shroud with the crew on the wire. I've never tried this on a boat of that era though. A concern would be that it would be easy to put all the extra load you've not dared to put n the shroud onto the checkstays!