The rules do allow such a readied Sneak Attack
The wording of that passage in grease is, in my mind, very unclear, but readied-action attacks and attacks of opportunity are at least two cases that clearly do work. They take place during the movement, so they definitely work. Readied actions basically take place whenever the person who readied the action wants it to, so you can definitely ready an action for “as he moves past me” rather than “right before he starts to move” if you like, and clearly the Rogue would like to.
As you note, this is a really difficult maneuver to use effectively. Worse, as the Rogue levels, there’s very little he can do to improve it; stuff like Two-Weapon Fighting et al., iteratives from extra BAB, and the like, aren’t going to work with it. So as he levels up, instead of getting to improve this tactic with his feats and other choices, all he can hope for is extra Sneak Attack dice – which aren’t going to keep up on their own.
Note, though: “he moves and remain at 5ft of the enemy in the grease area, and ready a 5ft step + attack with the same trigger,” doesn’t quite work: he could only ready that action if he had not moved already in the round. If he was already in position and did not need to move into it, then it would work.
I’d strongly consider reverting to the 3.5 rule
While grease was and still is one of the best possible standard actions you can take, this particular facet of the spell was a good thing, in my opinion. It encourages teamwork and is an excellent example of a Wizard helping his teammates shine, rather than stealing all the spotlight himself. If I was to nerf it, rather than removing this aspect, I’d most likely tone down the spell’s double-jeopardy nature, or its effectiveness even when the enemy saves and makes his check.
This particular rule is thus more of a nerf to Rogues (who, after all, could have easily gotten a wand of grease since as a 1st-level spell it’s fairly cheap, and they have UMD in-class) than it is to Wizards (who still have plenty of options). Rogues don’t need a nerf. In general, Pathfinder makes it decidedly more difficult for Rogues to get multiple Sneak Attacks per turn, and I don’t think that improves the game at all. It was, in fact, already too hard for them to do this in 3.5, in my opinion. So I’d strongly consider reverting to the 3.5 rule.
There are 2 definitions of "round" in 5e. There is the definition of "round" that you quote, which is from initiative position intMax to initiative position 0 (or negative if you manage that some how).
Then there is the definition used here for readied actions. This is the same definition used in "once per round" effects such as certain powers. This definition begins at the beginning of your turn and ends at the beginning of your next turn.
Because (unlike in 4e), readying an action and activating it, doesn't move your initiative order position, and because it matches the readied action refresh timer (which happens to use the same 1/round definition of round), readied actions can be used at any point in either the current round or the next round prior to your turn.
Here's how reactions refresh:
When you take a reaction, you can’t take another one until the start of your next turn. If the reaction interrupts another creature’s turn, that creature can continue its turn right after the reaction. (Player's Basic p70)
This is a large part of the support that leads me (and many others) to believe that readied actions can roll up to your next turn.
Best Answer
In general, readying an action can be used defensively, but only in certain situations. It's not a catch-all way to prevent ever being attacked in melee.
In example 1, you only become immune to the first person who needs to approach you in order to full attack you. This means that anyone who doesn't need to move (already adjacent, reach or ranged weapon, etc) can still full attack you. Likewise, once you react to one, your readied action is used up, and other people can still 5-foot up to you (or pounce you) and get their full-attacks in.
To make example 2 work, you'd need to ready an attack against the first person to attack you and 5-foot away after the attack. It works surprisingly well, but still has flaws. It still only works against people you can reach (so ranged and reach weapons still foil your strategy) and still only works against one foe per turn (so a team can still overcome you). Also note if the foe is already in reach when they start their turn, they can take their own 5-foot step and still complete their attack.
With either strategy, you are still giving up your own ability to make full-attacks, and once the opponents figure out what you're doing, they'll likely just avoid you since you only react when they approach/attack you, kill your party first, then come back to finish you off when they can surround you.
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