1. Stand tall with flexible upper spine
...instead of crunched, shoulders up, neck tight, upper spine stiff.
This will help you control your breath instead of pound it against your cords.
2. Move your head slightly back, chin level.
...This will open your throat channel.
3. Drop and move your jaw.
...Try a slight chewing motion as you hit and hold the note.
This can cause a huge difference because it allows the soft palate to lift.
Squeaking is for mouses. (Mice?) Let me know how this works for you.