I own a few logic analyzers (a couple of clones) and a Saleae Logic and a good enough o'scope (a Tektronics 2213) with a 60 MHz vertical amplifier bandwidth.
I also have about 50 years experience in electronics... Both mixed signal and RF...
One of the issues in the Audacity measurements is that they are analog in nature, Not digital so extracting the pulse width to any real accuracy is a matter of chance.. Particularly with the SDR as a measurement tool. Mine are based on the R280 chip and are better positioned as crude spectrum analyzers.. I enjoy very much playing about with them BUT I'd Never make an attempt at deriving accurate timing from them.. it simply isn't there.
Drift of the 35 MHz? (KHz) isn't really critical as the actual bandwidth for the detector is rather large. What is missing is the transition speed.. The Audacity measurements are effectively analog measurements that are capacitor coupled, Not DC coupled so one looses the accurate timing required to extract the pulse width's due to the effective 'spreading' of the pulses due to charging and discharging effects caused by the translation to the Audacity input as the sound card that translates this information to time related events is slewed by the measurement method itself..
Unfortunately a fair quality O'scope is still above $100.00.. This for a used good quality O'scope and well beyond the capacity of the various inexpensive "Digital Handheld Devices"... Unfortunately there is a steep learning curve required to using a device like an O'scope effectively.
That having been said the best method that I can see is to use a logic analyzer.. A cheap Alibaba clone is more than ample for your needs... However you will need direct DC measurements of the encoder to extract accurate timing information.
I would first measure the data at the key pin of the OOK transmitter or LED driver output with a logic analyzer to extract real time measurements before I tried to interpret the TX data as it is ground referenced and thus easier to accurately measure..
The drawback for many is the lack of the skills to identify the measurement point and the lack of both skill and equipment to do so with.
What I've seen so far look like faulty measurement techniques or PWM/PCM encoding and I suspect that this is not the real reason for failures in decoding these measurements. Likely more skewed data from the measurement techniques.
The CRC is really important and must be taken into account.. Basically Assume Nothing unless you can see the same results for any unique pulse train.
There has been a fair amount of investigation about IR encoders and decoders that can be had for a little imagination and a lot of searching.
This forum member might be of great help http://forum.arduino.cc/index.php?action=profile;u=193325
and this is a helpful Blog from him: http://bit.ly/1cvd0at