First, the lubricant may or may not be needed. In fact, it may not have helped at all, if they weren't counting on the blocks to be "self-propelled" by the gravity.

Secondly, a short lever of perhaps two cubits long would have been sufficient. The lever didn't "lift" the block, it just proved a small amount of push against the lower back corner. Granted, a longer lever provides more force, but the height restriction of the passage limits the length to no more than 2 cubits total. A 2-cubit lever, with a fulcrum perhaps 1 or 2 inches from the bottom edge, could provide an enormous amount of force for moving a block down a smooth slope of stone.

Likewide, if the block did get wedged in "kitty corner", it could be put into the opening on the side and levered back to center.

The 4 inch gap between two of the blocks suggests they pushed as far as they could, and may have even thought they had reached their goal, and then started pushing the next block into place behind it.

Anthony

You can lead a horse to water but you can't make him think.