Capacitor current leakage measurement using transimpedance amplifier
Looks like a good idea at first glance.  No immediately obvious "gotchas. 

Won't compete with the best test instruments but should be viable. 

I'd guess there would be some learning required along the way for a practical device. 



These two Burr Brown application notes were cited in your reference. Don't seem to specifically address the test issue BUT cover the high impedance fron end issues well enough that they will provide useful material. 

SBOA035 - 
PHOTODIODE MONITORING WITH OP AMP

SBOA060 - 
NOISE ANALYSIS OF FET TRANSIMPEDANCE AMPLIFIER