Is my limiting factor the output from my phone or the 3W speaker?
No doubt both are responsible. The phone doesn't provide enough audio power to the speaker, and the speaker is inefficiently coupled to the brain cavity.
...the speaker is making direct contact with the forehead, so using sealed ear couples isn’t an option for this project.
Why not? Just remove one of the them from the headband and press it against the forehead. Probably still won't be "loud" enough, but you can expand on the principle.
In any event, you need to acoustically isolate the sound emitted from the back of the speaker from the sound emitted from the front of the speaker. These two acoustic waves are 180 degrees out of phase with each other and will tend to cancel in open air. You correct this, normally, by placing the speaker in a sealed enclosure, with or without a tuning duct, and with or without internal sound-absorbing material inside the enclosure.
If a tuning duct is used (bass reflex design), the objective is to reverse the phase of the back-side acoustic wave so that it is emitted in-phase next to the front-side of the speaker and constructively adds to the front-side acoustic wave. A tuned duct is efficient, and ideal for use with a single audio tone, but the required dimensions for resonance may not be suitable for your purposes. Refer to any decent book on loudspeaker enclosure design, written in the previous century from about 1940 or later.
A less-efficient alternative is to mount the speaker in a sealed box filled with sound-absorbing material. Only the front-side of the speaker is exposed on the outside of the enclosure. The idea is to completely absorb all the sound energy emitted from the back-side of the speaker so there can be no destructive interference between the front-side acoustic wave and the back-side acoustic wave.
You then need a means to efficiently couple the front of the speaker to the patient's forehead, perhaps with a carefully shaped plastic pipe of suitable diameter to match the speaker on one end and a carefully sculpted opening to closely fit the forehead on the other end. You could use foam padding where the pipe contacts the patient's forehead to ensure a good acoutic seal. If it were my experiment, I would connect the 127 Hz sinusoidal source to a mains-operated audio amplifier. with perhaps as much as 100 watts capability driving a 4Ω speaker load. Include a volume control of course to adjust the speaker sound level.
If you eventually, through experimentation, find a level
and a frequency that "works" you can make measurements of the voltage applied to the loudspeaker and measure the current supplied to it too, thus determining the power required. Using this basic information, derived from actual experimental evidence, you can then decide how to proceed to make your "medical device hand-held and disposable battery operated."
Don't forget to apply for FDA approval and perhaps patent protection. Or not: sometimes the best approach with a successful new product is to just make and sell a boatload of them until a Pacific Rim competitor copies the product and sells it for one tenth your cost to manufacture.