Stop rhubarb compote juice from leaking
Consider two options:

Add a stabilizing agent for the compote: cornstarch immediately comes to mind, but I suppose sewit, or custard would do the trick. This automatically lends itself to needing a longer bake time which I can understand to be less favorable.

Try reducing more moisture while prepping the compote. By giving the rhubarb a longer cooking time, you can also intensify its flavor while getting a firmer, stickier compote.