How to find the envelope of a wide-band signal?
The analytical signal approach works very well for chirp signals. It stops working for mixtures of different tones. Taking the absolute value is a nonlinear operation that introduces cross terms and thus distorts you envelope.

I'd say that the envelope of a broad band signal as a property that is not well defined. First you need to define what you actually mean by that. Than you can come up with a method. For instance, the phase of a signal is not well defined for broad-band signals as well, because there exist two or more phases simultaneously. But depending on the actual problem you can come up with a special solution.

Just some notes to the phase example, because I'm an expert there. In physics there is the problem of defining a phase to measure phase synchronization of two or more broad-band systems. One solution is to compute the Lyapunov spectrum which measure phase synchronization implicitly without ever defining a concrete phase.

I just write that to make you think about what you actually want to know/measure/manipulate in order to step a bit back and have a more general look at your problem.