As per Heisenberg uncertainty, if you increase resolution in time, you loose resolution in frequency i.e. ,∆x*∆v >h/4π, which means to localise in time for 2 non-stationary signals, there has to be a trade-off. Yes, you're correct that wavelets solved this problem linearly.
HHT
As per your proposal, it will be great to see if your hypothesis stands true. I've known Hilbert Huang transform in other domain, i.e. in image compression. So, if you have 1 D signals, it should be just one dimensionality lower. And, hence should be specific case of it.
The MATLAB is a better tool for a rough draft, that can later be extended if required. This is also suitable for hypothesis testing.
EEMD
I've had the chance to read the papers of Zu et al 2005, 2009 regarding their approach to noise based signal analysis in them. However, I've not been aware of any libraries been implemented for specifically that purpose. This is highly mathematical and needs linear algebra libraries for optimization. Basically, an average is calculated by shifting a AWGN filter over the signal, where after many iterations only the original component of the signal is left.
Both HH and EEMD help in spatio-temporal analysis.
Approach:
1st : Derive the psudo code in pen and paper, and get verified
2nd : Test in MATLAB/ Octave
Kindly message me whenever you're free. If not online, shall reply ASAP.
Thank you!