I thlnk the enormous weight of something like three miles depth of strata would have forced the water out of the lower layers and hardened them quite rapid
Alas, measurements of how fast water moves in rocks or lithifying sediments show the opposite. The pores through which the water must move are squashed down to being infinitesimal and water just cannot move through them quickly.
You are also forgetting that lithification involves chemical reactions which are not noticeably sped up by pressure.
Your second paragraph is all argument from your personal and ignorance-based incredulity. We work with evidence.
Chemical lithification doesn't need thousands of years
Really? Show us a citation.
And if you squash pores what happens to the water in them?
Water is essentially incompressible, so any gas would be compressed to essentially zero volume until there was only water that doesn't change volume. Except for any edges exposed to the atmosphere (very rare) the pressure would be almost perfectly hydrostatic (acting equally in all directions -- see Newton's second law). The hydrostatic component of stress does not move the water. The non-hydrostatic component does move the water, very slowly, through pores so small that the frictio of the water against the solid wall is significant, resisting the motion. It moves somewhere between a few yards per day and and an inch per century, depending on lots of factors... although lithifying rocks tend toward the slower end because of the very small pore sizes.