You are right, multiple discontinuities along a transmission line will reflect and cause confusion. Make sure the signal source itself is well matched to 50 ohms, so you do not get re-reflections at the source!
BUT you might be able to gate out the spurious reflections, and concentrate only on the one reflection you want.
Other than that, things get complicated in a hurry, as you would need to dump it all into some DSP board, and employ multichannel cancelation techniques, possibly with a more complicated waveform such as a frequency ramp, or OFDM signal, etc.