Will the detent not budge or will the detent depress and the sight post not turn?
Just for kicks, look at the front of the front sight post and make sure a National Match type front sight post wasn't used on your rifle.
These front sight posts have and allen head screw that turns in and locks the front sight adjustment so that nobody can fiddle with the sight settings once adjusted.
If that screw is there you will need to back it off before the detent will depress or the front sight will turn.
If that little part isn't present and,,,,,,,,
Since you applied oil and let us figure everything is still froze up, so, try this,,,
Use a 1/16" or a 3/32" PIN PUNCH, skip the nail, it is probably too large in diameter to fully depress the detent,,,use the pin punch and a light hammer to tap on the detent until it moves freely, up and down on the spring.
Once the detent is free and moving and you can fully depress it, you should be able to move the front sight post with fairly light pressure.
If the front sight post still won't move with the detent fully depressed try this,
depress the detent with the pin punch then angle the punch so it is against the side wall of the detent notch on the front sight post,,,use the light hammer to gently tap the punch against the post notch, this should free the post enough to allow it to turn freely.
I don't believe the front sight tool offered by Bushmaster will work any better than any other until you clearance the sides of the sight ears but I may be wrong on this.
Good luck, sounds like you got the front sight from hades on your hands.