Our approach is very similar but we use different tools. I use MySword Bible on my phone. It gives me the ability to compare various translations side-by-side as well as a hot link to the actual parsings of the Greek text and Strong # definitions.
It's true the goal is first to identify translation bias and then decide which might be the "best" translation. A simple, side-by-side display of various translations is usually enough to expose bias. Landing on an acceptable translation is a bit more tricky.
For me the most effective way has been to simply read the verses to obtain the facts which are stated. I don't read to obtain an understanding or interpretation. I don't perform an academic analysis (the reference sources are too biased ;-) I find that after I have the facts then the understanding the follows naturally.
(I do admit that the fact finding can get a bit technical at times but it's also fun ;-)