tikz-qtree inside gb4e example not centered when bidi is loaded

Question

I am using tikz-qtree to draw syntax trees that go inside of gb4e examples. I was very happy that I was able to get them to center by following this answer: Centering trees

However, I then decided that I wanted to use some Arabic text in my paper, so I loaded Arabic as the other language via polyglossia. Suddenly, none of my trees were centered. I'm guessing that the problem has something to do with loading bidi, which polyglossia does when you add a right-to-left language, but I'm not sure how to get around it.

Here is a MWE:

\documentclass{article}
\usepackage{tikz-qtree}
\usepackage{polyglossia}
\setmainlanguage{english}
% Uncomment the following line to see the problem behavior:
%\setotherlanguage{arabic}
\usepackage{gb4e}

\begin{document}
Here is an example tree that I want to be centered.
\begin{exe}
    \ex
    \hfil
    \begin{tikzpicture}[baseline]
        \Tree [.DP
                [.D the ]
                [.NP [.N center ] ] ]
    \end{tikzpicture}
    \hfil
\end{exe}
\end{document}

Here is a photo of the desired output:

And here is the output I get when bidi is loaded:

Answer 1

The original poster is my student, so I met with him in person to debug this problem since none of the commenters were able to replicate the issue he reported.

It turns out that the problem is not specific to tikz-qtree or gb4e. It is caused by a bug in older versions of bidi (previously reported here) that interferes with the tikzpicture environment of tikz. With these older versions of bidi, you can see the effect in any list environment, not just gb4e's exe environment.

There are two solutions:

1. Update bidi to the current version, which no longer has the bug. In general this is what I would recommend, but Aidan has opted not to do this for now because he is nearly finished writing a thesis and doesn't want other things in his setup to break.
2. Surround the tikzpicture environment in a \makebox{}, as suggested in this answer.