How to eliminate early effect in constant current source
The best way to circumvent the dependance on VA is through cascode mirroring. These have the effect of somewhat pinning the collector voltage on the output transistor so that most of the dependence on VA is removed because Vce won't be changing much on the bottom two transistors in the mirror.
It's an awfully low value for an early voltage, but likely not a problem for uses like a switch or a simple amplifier. The reason the early voltage is so low is because that transistor is designed for 200-300 Volts. Designing transistors to handle such extreme conditions requires design trade-offs. In this case, the gain and early voltage aren't that great.
Unless you're designing an integrated circuit most designers don't really have a use/need for it. You generally need matched transistors to perform what you're designing and discrete parts are hardly ever matched so adding in VA isn't going to help anything. This seems more like an issue of the right tool for the right job.
The impedance of the output side of a current mirror is completely dependent upon the Early Voltage as you can see here: http://users.ece.gatech.edu/phasler/Courses/ECE4430/Unit2/Current_Mirrors.pdf so there's no way around determining the output resistance if you don't know the early voltage. If you're using a simulator, you can plot the Vce vs Ic graphs and then determine the early voltage from a couple regression lines as seen here: http://en.wikipedia.org/wiki/Early_effect


In summary, I'd use different transistors to build a differential amp and go with a cascode current mirror.