Use a low value shunt resistor, preferably on the low side, add in a 200kHz bandwidth amplifier across the shunt resistor and use 2 oscilloscope channels: one for the low range (taken from the amp) and one for the upper range (taken straight from the resistor).
You can leave that as is, or if you want to, you can post process that data, it's simple: export from the oscilloscope to a file format you can manage easily, like CSV. This way you could write a nice little program that "glues" together both channels, using the data and resolution sensitive channel whenever possible.
Then the algorithm is the following (assuming Ch1 is for the low current range and Ch2 is for the high current range:
1: Read values from both channel tables
2: T=0, T will be the time in which a sample is taken
3: Read Ch1 and Ch2 at Time position
4: If Ch1 voltage is less than 90% of its maximum value, then copy its voltage into the Output table, at the Tposition (the 90% thing is because oscilloscopes take some time to recover from having their inputs saturated, so the 90% gives some margin for recovery)
5: Else, copy the voltage of Ch2 into the Output table, at T position
6: Increment T
7:If not finished, go to 3
That should give you resolution where you actually need it plus a lot of range too. It *could* be done in Excel, if there is a function for decision making or selecting data from one source or another depending on something.
The sensitivity of the lower channel depends on the amplifier gain and noise and the maximum range of the upped channel depend on how much voltage you can drop across the shunt resistor. For best sensitivity select the highest value shunt resistor you can get without disturbing the circuit, and get a high gain, high bandwidth op-amp for the low range. I suggest Analog Devices and Linear Technologies parts.
I would also recommend either having a PCB designed for it, or using this technique:
https://www.google.com.do/search?q=copper+clad+rf+prototyping&espv=2&biw=1600&bih=775&source=lnms&tbm=isch&sa=X&ei=y468VMP3LoXQggSA04KABg&ved=0CAYQ_AUoAQ#imgdii=_&imgrc=26mgLjEdfdo2QM%253A%3BIVcZN82d0DwkwM%3Bhttp%253A%252F%252Fwww.aholme.co.uk%252FSpecAnHtml%252F7a_70.jpg%3Bhttp%253A%252F%252Fwww.aholme.co.uk%252FSpecAnHtml%252FSpecAn.htm%3B512%3B384Remember we are talking about a high performance op-amp, so read the datasheet recommendations and application information because all the important stuff is there.