I agree that the 2nd law is pretty much a statement about statistics - and the 1st law is just a restatement of the conservation laws.
The issue of whether the 1st law might be incorrect is interesting.
Obviously, science knows of no situations where mass/energy is not conserved - and discovering such a situation would be a truly monumental discovery...perhaps more important than things like relativity.
What this means for the perpetual motion nuts is more nuanced.
Firstly, the realms of physics which are attainable by amateur tinkerers are very well explored indeed - there is simply no possibility that some fiendishly clever arrangement of mechanical parts, magnets, coils, hydrogen flames, water electrolysis and so forth is going to break the most fundamental law of physics we know of. All of the science involved in those systems are far too deeply explored and well-understood for that.
If a perpetual motion machine (or anything else that breaks the 1st law) is possible - it's going to be far outside the realms of normal existence - something in the quantum range - or involving black holes and singularities of other kinds - gravity waves, dark matter/energy - things that AREN'T well-understood yet. Sadly, these are things that lie outside the range of amateur tinkerers.
It's possible to overturn major scientific laws - as Einstein did to Newton's laws of motion. But (as with Einstein) - you have to do that outside the realms that have already been tested. When Einstein proposed relativity - we did not have the ability to send super-precise clocks out into orbit to measure how they fared in reduced gravity and high relative velocities - and the flaws in Newton's laws only show up under those kinds of extreme situation.
If the flaws in Newton's laws were noticeable in the realms that amateur tinkerers could reach - they'd have been overturned a century earlier - but only with advanced technology could we actually prove that Einstein was right.
The same thing happened with conservation-of-energy - every experiment open to a Victorian scientist shows that energy is indeed perfectly conserved. It's only when you have nuclear reactors and exotic radioactive materials that the fact that energy can be interchanged with mass became evident that caused us to have to talk about "the conservation of mass/energy" instead. Again, the experimental evidence to overturn this very old "law" only came about with cutting edge instruments and experiments that the average person could never undertake.
So these tinkerers with magnets and such are really wasting their time. It's probably impossible to make a perpetual motion machine - but if there will EVER be a machine that breaks the 1st law of thermodynamics, it'll have something exceedingly exotic going on inside...and it'll come from the bowels of a research lab - or perhaps a cosmologist's telescope.