Disclaimer: What follows is my own interpretation that I have not seen in any commentaries, so feel free to be skeptical of it.
Summary: The difference between the question and the answer is that the question assumes we are dealing with a true gezeirah shavah, while the answer rejects that assumption.
I would suggest that Tosafos's answer is that we are not dealing with a true gezeirah shava. A true gezeirah shavah links two cases that would not necessarily be related, and tells us that the same law (or laws) that apply to one case apply to the other case. Tosafos's question assumes that this is a true gezeirah shavah. As such, the law that women are exempt from tefillin should carry over to balding themselves.
Tosafos's answer then comes and says that this is not a true gezeirah shavah. Rather, this is simply an example of using one case to figure out what an ambiguous term means. The term "between your eyes" is ambiguous. When it comes to tefillin we are unsure what it means. Does it mean that the tefillin must be on your forehead between your eyes, or does it mean that the tefillin should be on the top of your head?
We can use the case of balding to determine what the ambiguous term means. As Rashi (ד"ה תפילין) explains, when it comes to balding it is obvious that the prohibition of balding must apply to an area where there is hair. As there is no hair on the forehead, "between your eyes" perforce cannot mean "on your forehead". Once we know from the case of balding that "between your eyes" does not refer to the forehead, we can go back to tefillin and determine that since the tefillin are supposed to be "between your eyes" it must be somewhere on top of your head and not on your forehead.
In other words, no law was derived from the case of balding. The only thing we used that case for was to figure out what a term meant. We arrived at the law for tefillin not via applying a law from balding, but by simply reading the Torah with our newfound knowledge of definitions.
Since you mentioned Tosafos HaRosh, I would argue that this fits particularly well into the language used there:
דקסבר דלא נאמרה ג"ש ללמד חיוב ופטור אלא לפרש היכן הוא בין העינים
For he holds that the gezeirah shavah was not said to teach obligation or exemption, but to explain where "between your eyes" is.
I.e. the gezeirah shavah was not to teach us any laws, but to define a term.
Now let's see if this explanation can fit with the remainder of Tosafos (not mentioned in the question). Following this understanding, Tosafos then asks why tefillin cannot be placed anywhere on the head. If the term "between your eyes" can be defined by what it means in the case of balding, then tefillin should be able to be worn anywhere on the head just like the prohibition of balding applies to anywhere on the head.
This, I believe, fits with the above explanation. If we can use the case of balding to define the term "between your eyes" we can't select only half of the definition to apply to tefillin. We have to accept the entire definition, which should lead to the conclusion that tefillin can be worn anywhere on the head, since that is the full extent of what "between your eyes" means.
Tosafos then answers this question by saying that if it was true that tefillin can be worn anywhere on the head, why did the Torah write "between your eyes"? It should have simply written "on your head". Thus, we do accept the entirety of the definition gleaned from the case of balding, but there is an external reason why tefillin cannot be worn anywhere on the head, namely, because there is an implicit exclusion of the rest of the head by the fact that the Torah chose not to use the term "on your head".
This, too, fits with the above explanation. Tosafos is still holding to the idea that the "gezeirah shavah" is really just a definition, and we can still explain how the laws of tefillin can seem to not incorporate the entirety of the definition.
Then Tosafos has a follow-up question on this latest answer. If it is true that the Torah's use of "between your eyes" instead of using "on your head" is an implicit exclusion of the rest of the head (even though the term "between your eyes" technically includes the entire head), why don't we make the same argument in the case of balding and say that the prohibition does not apply to the entire head because if it did then the Torah would have used the term "on your head"?
Again, this still fits with the above understanding. Tosafos is merely testing whether the latest answer is actually a valid answer, and it appears that it is not.
Tosafos then answers this question as well, by saying that while it is true that in a vacuum the non-use of "on your head" would be an implicit exclusion of the rest of the head, when there is a specific reason to not use the term "on your head" this implication would not hold true. In the case of balding there is a specific reason to not use the term "on your head", namely, that by using "on your head" we would lose the opportunity of using the case of balding to figure out what "between your eyes means". We would then be stuck in the case of tefillin not knowing that "between your eyes” does not refer to the forehead. Thus, the Torah was "forced" to use the term "between your eyes" for an external reason; therefore, the failure to use the term "on your head" cannot be taken as an implication that the rest of the head is excluded.
This last answer also fits with the idea that the gezeirah shavah was not a true gezeirah shavah. When all the dust settles there are still no laws being transferred from one case to the other. All that has happened is that we have used the definitional knowledge gleaned from one case to understand the text in another case, and the Torah was written this way deliberately to allow us to glean that knowledge.