I tried measuring the same transistors a few times and it almost every time gave me different vbe lol, from 678-692 :S
The AVR Transistor Tester design isn't intended as a precision device, and no clone to date uses the 0.1% resistors or the 0.1% voltage reference specified in the documentation. The software is very impressive for it's capabilities with simple hardware.
Like most clones you probably have a relatively large difference between the probing resistors on each ADC sensing pin. The software can only have one value attached to the 680R and 470k probing resistors. This is why the design specifies 0.1% resistors. In this case it is the tollerence that matters, not the accuracy. Each 680R/470k resistor needs to be closely matched, but it doesn't matter if the resistance is extremely accurate. The variance between channels is important. Your voltage reference is also creating accuracy error because the reading that the TT is giving you assumes you've used a 2.5 volt reference with 0.1% accuracy. The TL431A reference used in clones has a tolerance 10 times larger than the specified accuracy of the design as listed in the documentation.
(Edit:
A cheap replacement voltage reference option is here. I haven't tested them yet, but that's what I ordered to try on an SMT clone. The pinout is different than the TL431A, but the LM4040 DS says you can leave the Vref pin floating, so it should work by simply soldering it diagonally without a jumper or other mods.)
I was under the impression that we need to stair step the voltages to gather a more 3 dimensional understanding of transistor Hfe and Vbe curves for matching. If you have an oscilloscope Allen has some great tutorials on different ways to build a simple curve tracer on his A2AEW YouTube channel. Specifically his videos numbered #232, #197, and #49.
My curiosity about curve tracers is if there is any potential to add one as a project option to the AVR TT. I know people have created "Arduino" oscilloscopes that will run on controllers as small as the ATmega8. I wonder if we use one or two 74HC4052's (dual 4 channel analog MUX/DEMUX) and reconfigure the Zener threshold DC to DC boost converter, could we create a curve tracer option?
I've seen one project on YouTube that used an Arduino oscilloscope reconfigured in a XY mode to create a curve tracer. (Thinking out loud here) I wonder if a 4052 could be used to control a feedback resistor network on a DC converter while expanding the AVR's I/O and protecting it from over voltage/current.