Z-plane Elastique is indeed patented, but no one seems to know how it works. However, when it comes to other Time Scale Modification algorithms, I can help out there (It's my PhD area).
Elastique doesn't just interpolate between points as it maintains the pitch of the audio being interpolated.
For a basic explanation, TSM algorithms work by framing the signal and then manipulating the ratio between the analysis shift/hop and the synthesis shift/hop. The differences between methods is how each tries to maintain coherence within the signal.
Generally, methods are broken into Frequency domain and Time domain methods, each with strengths and weaknesses. Frequency domain methods are better with harmonic and complex material, where as Time domain methods are generally better with transient rich material. The Phase Vocoder and extensions (Flanagan and Golden, Portnoff, Laroche and Dolson etc) make up most of the frequency domain methods. These methods modify the phase progression between frames to maintain horizontal phase coherence. OLA and it's extensions SOLA, WSOLA, etc (Roucos and Wilgus, Verhelst and Roelands) maintain coherence by overlapping frames at points of maximal similarity.
For implementing TSM on the axoloti, I would first look at trying to implement the SOLA algorithm (Roucos S. and Wilgus A.M., “High Quality Time-Scale Modification for Speech”, IEEE International Conference on Acoustics, Speech and Signal Processing, pp. 493-496, March 1985).
If there is an efficient FFT on the Axoloti (I haven't looked in a long time), the phase vocoder should also be possible.
If you would like to see some MATLAB code of these and other methods, check out my github at www.github.com/zygurt/TSM . I also have some algorithms on there that will be published within the next fortnight. Frequency Dependent Time-Scale Modification allows for time scaling of multiple frequency ranges by different amounts. This one definitely won't work on the axoloti.
When considering real time, you will run into restrictions regarding the amount of memory available. My advice would be to write the algorithm and then assign the rest of the available memory as a circular buffer.
I hope this all helps. Let me know if you want clarification on anything.