One Orog gets pinned (Sentinel). The other one then dashes away into the other room.
Next up is the Ranger who moves 35' into the room where he positions himself to be able to see the survivor through the 10' doorway (cover is irrelevant as he's a sharpshooter), Hunters Marks it, shoots twice, and as it's already badly wounded, likely killing it.
To start with why does the bladesinger need to use shield? According to you earlier the enemy would "ignore" her, but instead of "ignoring", they use every single action they have in the first round to attack her? You just contridicted yourself. As a matter of fact the argument was not only that they would ignore her, but that would ignore her to attack others and beat the party in terms of action economy ..... but you are not doing that either. Also nowhere in the description of dodge does it say you are "leaping around" you are probably waiting for the enemy to get close or lanuch an attack to do something like that, but even if it is I hardly think 6 aggressive orcs are going to be scared off by a leaping, dodging, dancing elf.
The Ranger can't shoot the fleeing orog unless the DM is stupid. The orog is going to move to the side to avoid getting shot at. The Ranger is 30' into the hallway with allies in front of him in the hallway (difficult terrain to move through them or uses extra movement to go around them). This savant Orog is smart enough to know a lone elf in a doorway is unhittable just by looking at her but he is too stupid to know to move to the side while fleeing to get full cover? If you were playing the enemy smart instead of trying to make a point and take away player agency he would move to the side and the only person who could target him is MAYBE the Rogue and that is after taking dash as a BA and without a sneak attack and to even do that assumes the wizard and the immobilized Orog in the room are positioned so he does not have to go through or around them. Oh and by the way now in terms of rolls - lets see with fireball I managaged to kill all 4 orcs and the Orog that got away missed his save. I managed to hit the Orog that might have saved on fireball with sentinel, the Ranger managed to hit and get enough damage to kill the fleeing Orog too stupid to take cover. Finally, let's point out the wizard needs to go into melee range for that corner condition where I can stop them with fireball, great rolls, and a stupid Orog to even be possible. She can't stop them from fleeing if she "acts like a proper wizard should" and stays back out of melee after the fireball.
The whole point of your original position is it is never a help for the party for the bladesinger to dodge and keep the enemy off other players. You set up a scenario, tried to prove you point with the enemy getting great initiative rolls, when it didn't work, you changed your tactics to get a "bad" outcome for the party but one which is completely irrelevant to your original claim concerning combat and action encomy.
Your original argument was NOT that bladesong and dodge allows an enemy to flee from a battle and alert the complex, it was that the enemy will ignore her and she does not contribute to the fight.
You argued that it would help the enemy win the fight or at least do better in the fight based on action economy and the bladesinger taking a useless action. That is what YOU said would happen, it didn't happen and you didn't even try to support that claim. As a matter of fact all the attacks they did launch targeted the bladesinger who they were supposedly going to "ignore". What you really see and don't want to admit is bladesong+dodge in this scenario, or in many others like it, puts the party way AHEAD on action economy forcing the enemy to use actions on things like overun, grapple or futile attacks with very little chance of hitting. Meanwhile the party pulverizes them with damage from range. You know it, it has been made abundantly clear but you don't want to admit it.
New game - it is a 40x40 foot barracks with a 3' door 2 Orogs and 4 Orcs and no exit. Bladesinger opens it positions herslef in the doorway does bladesong.
This is a much better scenario to evaluate YOUR argument because they can't avoid a fight and we can evaluate your claims that this hurts the party in terms of action economy. Try to support your actual argument now.
Lets play!