Matched filter for variable time scaling?
One first quick and dirty method could be to first store a sort of scale-space library of your original waveform $w(t)$, computed  at different scales (discretized), and then perform a "filter bank" of matched filters in parallel on the same observed signal. This proposition is a kind of  dual of the non-feasible solution you evoked. This way, you can save time from having the waveform scaled offline, and do not have to it on the signal. Then, you would probably have to detect the best match at a given time. Ambiguities may appear by superposition: at a given time $t_0$, the signal could look like $a w(t-t_0) + b w\left(\frac{t-t_0}{s}\right)$, where $s$ is a scale parameter.

To see how much better could an offline solution be, you may have a look at a scale-invariant matched filter. Thanks to you question, I just discovered the recent paper:  The Mellin Matched Filter, A. Monakov, 2015:


  In propagation channels signals are undergone translation and dilation
  changes. The Fourier and Mellin transforms are natural foundations of
  the analysis of wideband signals. Three interconnected problems, where
  the Mellin transform plays a key role, are considered in the paper: i)
  synthesis of a linear matched filter that is invariant to signal
  scale; ii) estimation of the signal scale; and iii) the wideband
  ambiguity function and its properties. The filter that is invariant to
  the signal scale and maximizes the output SNR is synthesized in the
  paper using the Mellin transform. The filter is named the Mellin
  matched filter. Introduction of the Mellin matched filter allows to
  give a new interpretation of the signal scale estimation and the
  wideband ambiguity function. Concept of the Mellin matched filter
  facilitates to produce a physical interpretation of the resolution of
  wideband signals and the time-frequency-scale uncertainties.


I have no idea about how it performs in practice.