As for the extra rod/screw et al - well, there is a number of approaches. You could do any of the suggestions you had, but just some thoughts:
a multi-spar scissor action wont be quick by any stretch of the imagination and getting it to stay square will be a bugger... but you could do it.
The extra threaded rod is doable, but seems to be overkill as the issue isn't exactly one of torque.. which leads to
Adding a support arrangement to the front has been done - some have done extension springs from the front to the back of the bed frame, which whilst it wont 'solve' any lateral movement, will 'preload' the platform so it remains in a constant state - tune out the angle, and it should be constant...
Then there is the 'brace from the front sides' approach - just basically think Angle-Bracket across the front of the bed and then with rollers (or bearing) run it up and down the inside lip of the front vertical frame supports
There is posts for all the above suggested mods here on the forum already (excepting the scissor suggestion).
Of course - the main problem with the SD platforms in general is that they only run self-aligning sintered bushings... not bearings.. and these will also occasionally develop slop in the wooden platforms leading to the platform 'leaning downwards' from the front ledge... The solution here is to; replace the self-aligning bushings (cheap, easy, buys you another 6-12mths...); or replace it with appropriate imperial sized bearings (good luck - was a no goer this side of the Hemisphere - but given the UK is only one of 4 countries that still use Imperial, you should have better luck). One final option is switch to metric rods and use some LM10UU's or similar on the bed - however, there is a fair bit of work getting the bearings fitted to the bed. Wooden will be easier here, as the ALU requires some fairly major rework to fit the bearings in...
Anyway - just some ideas/thoughts/dribble from myself 