Interesting thread.
Some suggestions are very neat, others over-worked (IMO). The first rule, after all, is:
keep it simple.
Don't believe those who tell you you need to complexify your game because you don't want to use a battle mat and minis!
Flanking: Agreed - easy to fix:
1) Whenever you're 2-on-1 you can flank.
2) Whenever the DM feels it's appropriate, you flank.
I expect flanking to occur about as often as in the RAW, meaning classes that rely on flanking shouldn't become noticeably weaker (or more powerful). Remember that already in the RAW, the frequency of flanking opportunities vary wildly with different DMs, different adventures and different tactics, so it ain't as if there is a given norm your world must adhere to!
Push/pull: instead of these effects giving their benefits depending on exactly where everybody are positioned, make it simpler and more abstract:
1) the easy case is when you can benefit directly from pushing your foes into a harmful terrain feature (such as "thin air"). This works exactly the same - make a save or eat pain.
2) then we have the case where pushs/pulls can be made to gain a situational benefit. Instead of "parking" enemies in areas where they can be flanked or area attacked, you simply give bonuses for successfully pulling/pushing them around. Perhaps you get a +1 bonus to attack them. Perhaps they get a -2 penalty if you slam them into a bunch of chairs, a fireplace or a stack of crates?
3) the final case is when these effects are intended to make you enter melee or force you away from melee. (Artillery effects push you away; Soldiers pull you in) Again, it shouldn't be too hard to describe this in the abstract.
Generally, just tell your players they should expect a little less utility from any power with push/pull and especially slides as their main benefit. Expect them to select fewer such powers. This is okay, and shouldn't necessitate a re-write of the rules.
Ranged and Area effects: we have run these for decades without battle mats, so I don't expect there to be anything that needs changing in 4E!
Opportunity Attacks: again, instead of looking at the map, look at the action. With prior 3E it should be easy and intuitive both for the player and the DM to tell when an OA is triggered. Again, no battle map needed.
Be generous in awarding situational modifiers to encourage colorful descriptions that lessen the "grind". Was it Stalker0 who did a write-up on "combat skill challenges"? Seems like a useful thing to have in a minis-less game!