I’m not sure you can say that once you put it on Bihetter you may keep it on, since we find by Kohanim that they must remove it after the Avoda, because of the Klayim. However, like I said earlier, they are allowed to keep it on for the amount of time it takes to get it off normally. Here too, perhaps it is Muttar to keep it on into the night for the amount of time that people normally wear day cloths at night. As a proof to this, the reason the Talmidim didn’t put on Tzitzis was because someone might put it on at night. If you must throw it off at dusk, isn’t that a much closer Chashash, that someone might leave it on?
As for your Stira in Rashi, the Bach has an approach that explains Rashi to hold that it goes by the Begged. Where he says, he might put it on at night, it means, he might use it as a night garment.