I think the answer depends on whether the load on the screw is in tension or shear. You won't be able to install a self-tapping screw unless you make the pilot hole pretty large, so the thread grip will be small. Therefore, I don't think the self-tapping screw (of the same nominal size) will be anywhere near as strong in tension (pulling straight out). It might be adequate in shear (pulling sideways across the diameter), but if the load causes the screw to wobble in the hole too many times, it will eventually fail.

The above is my considered opinion, but I have not attempted to research any hard data on the subject.

You can buy tap and die sets rather inexpensively that will work well in aluminum, but may not be so great for harder steel alloys. Tap with a lubricating oil and when installing the screws, use a good locking compound or one like Tef-gel which is primarily to electrically isolate the (assumed) stainless steel screw from the aluminum mast. Failure to do that will eventually allow corrosion of the aluminum near the screws.

I have not seen the Good Old Boat method. My Lazy Jacks only have connections on the mast and boom. Seems like tying them into the spreaders adds considerable complexity. To relieve any possibility of chafe the bitter ends of mine are long enough that I can pull the lazy jacks forward and secure to the mast. That also helps when taking the mainsail on and off.