It's not a problem that I would claim to be an expert in, other than knowing members fairly well, but no, I think there is no creative way out of it.
Some travel by members is paid for by the House, and we do not publish it immediately. Some of it we publish only in total and not in detail and publish later, either quarterly, annually, or on request, although under the freedom of information regime, which I think is similar to yours, not everybody asks all the time.
I think it's the immediacy of something appearing on a website that causes people concern. Saying “Yes, in the course of the year, I got £900 so that my partner or dependent child could be with me for some days at Westminster” is less embarrassing than someone saying “Oh, I see that yesterday there was another £42 gone on bringing whomever down to London.” That's an impression I have.