The prohibitions which Ashkenazim take on themselves during the nine days seem to spring from post-Talmudic thinking and application of the notion of "reduced joy." For some reason, the particulars (laundering, swimming etc) were chosen. The custom not to eat meat or drink wine (developing from selectively applying the practices in Bava Batra 60b )was also applied. During a seudat mitzvah, we are allowed (required or not has been discussed) to eat meat and drink wine so the level of heter has to be more persuasive than the level of the issur and yet this prohibitive-minhag at least is grounded in a specific type of activity discussed in the gemara. Why is the level of heter not then considered more powerful than the prohibitions we take on as minhagim beyond meat eating, ones which are not mentioned in the gemara?
If you say that the prohibition of meat/wine stems from the connection between them and terms for simcha (contraindicated in a time of sadness) then, not only does that ignore the Bava Batra logic of meat/wine=korban, but it opens up the door to logic and wordplay which would connect bathing, wearing clean bigdei chag or hair cutting to simcha as well [no, I don't have the actual words yet, but if I could be empowered to find the connection, I would, and I'd throw a rocking barber-party next week].
In summary, once a seudat mitzvah can push aside the talmudic not eating meat, why can't it push aside other seemingly arbitrary minhagim of "sadness."