I'm not even convinced (hence the conditional at the start of my post) that Twin Strike is a valid power to use for the TWFl OA.
Heavy Blade Opportunity says "When you make an OA with a Heavy Blade". If you use Twin Strike as your power, you're making an OA with two weapons. Let's say they're both longswords; it's an OA with two Heavy Blades, not an OA with a Heavy Blade.
It doesn't matter that one is using Twin Strikes. One of the attacks within Twin Strikes is still an OA with a Heavy Blade and because of that, feats trigger.
I think it is legal.
1) OA occurs.
2) Take first OA with main weapon and hit.
3) Two-Weapon Flurry kicks in: "While holding a melee weapon in each hand (check), if you make a successful opportunity attack with your primary weapon (check), you can also make an opportunity attack with your off-hand weapon (check) against that same target (at -5)"
4) Off hand attack is OA and at -5, so Heavy Blade Opportunity can be used: "When you make an opportunity attack with a heavy blade (check, it doesn't matter that it is the off hand, it is still an OA with a heavy blade), you can use an at-will attack that has the weapon keyword instead of a basic attack." Twin Weapon is selected.
5) HBO replaces a basic attack with a Twin Weapon attack, but it is still a OA. The fact that a basic attack gets replaced with an At-Will attack does not change the fact that it is still an OA and it is still at -5.
6) The first OA attack of Twin Weapon at -5 hits. Go to #3 and start cycle for it, but these attacks are still OAs, but at -10 now.
7) The second OA attack of Twin Weapon at -5 hits (or does not hit). This is an off-hand attack, so #3 does not apply. Note: can go to #4 here instead of swinging.
Or, the order can be changed. Instead of step #2, HBO can be used immediately to replace the OA with a Twin Strike OA, but that would do less damage on the first attack, but a better to hit on the first off hand attack.
I think it is legal. I think it is fine for level 21 and 3 feats. And, it is eventually self defeating.
The version I have here is different than what the OP posted and is a bit unusual in that the #7 attack is an extra attack each time (as opposed to using #7 with HBO, it replaces #6 with #3).
I'm not quite seeing your claims that the OAs are not OAs. Nothing in the feats indicate that the attacks are not still OAs. You have nothing explicit in your interpretation that illustrates that the property of OA is removed. #5 is the key here.
I do not see where this is illegal or where this is unbalanced. Sooner or later, the PC will miss with the primary hand because of the stacking penalties. #7 can be used to extend this a bit by replacing it with HBO, but even then, it will still eventually fail. Also, normal basic attacks will be replaced with Twin Strike attacks (i.e. no Str damage).
In fact, the PC will be lucky to get 5 attacks in, typically 7 at the very most. He could miss with attack #2.