To the OP, another consideration that may not apply to your case is whether there is more than 1 independent claim, especially if there is another indep containing the 4-button limitation, whereas the 1-button claim contains any other limitation differing from the indep having the 4-button limitation. This would give them more room to try to argue that their prior statements re the 3-button art were intended toward that other claim.**
Otherwise, subject to limited understanding of a fictionalized/simplified case, I would probably use PHE as a non-infringement prong of the analysis (despite what "looks like" literal infringement, and understanding your concern about using it outside of DOE), but I would also complete the invalidity prong for the scenario where the claim might be construed to require fewer than 4 buttons.
I've seen Markman rulings where a limitation such as "having a sine wave cycle" which appeared to be directly infringed by a product having one sine wave cycle was not infringed because, after a PHE analysis the phrase "having a sine wave cycle" was held to be "having at least 2 sine wave cycles". The PHE was based on statements in the spec and arguments in prosecution.
** The other reason I asked about additional indeps is, I've had to analyze similar sounding file wrappers that ended up with a granted claim clearly contradictory to the applicant's argumentation, but in those cases the contradictory claim was usually claim 63 following independent claims 1, 19, 35, and 42 not being contradictory. In one really egregious case, the applicant deleted the relevant term from the claims, and after the next rejection put it back into all of the indeps except one of them, while telling the examiner that the term had been reinserted "into the claims" (did not say "into all the claims").