Not really. The entire works of the New Testament were written within 1 generation of the death of Jesus. All the works were written between 50-100AD. We also have manuscripts and fragments of the New Testament books that circumvented government and religious organizations, that have been translated from the original languages. Said copies are available, and are used to compare against your supposed "government/religious organization" translations.

I suggest you do a bit of research on textual criticism and the manuscripts that make up the New Testament. Its a bit different than you make it out to be. Just because the major unical codices were authorized by Constantine and others does not mean there aren't earlier fragments available that can be referenced when creating a new Bible. The reality is that the fragments that predate the unical codices agree with them, challenging your argument that they are somehow modified from their original intent. We have fragments of almost every New Testament book that predates Constantine and the Catholic church.

Here's an example: http://en.wikipedia.org/wiki/Papyrus_52

The fragment's date? 125AD - less than 100 years after the death of Jesus, and only about 30 years after the date of the writing it references (Gospel of John).

By your own source the date of that fragment of a scroll could easily be 150 years after.  There is plenty of controversy regarding it and they are guessing it was written in 2nd century.

Either way, nothing was written down directly and it was people who heard, from someone else, who heard from someone else - and that is from the most direct case we know of.  Most are much more remote.

Plus, several things were thrown out by Constantine. 

Not sure why you would even disagree about the translations.  That's just simple fact and taking things out of context always distorts things and bring in room for error.  Example, did you know in Greek there a 4 different words for what we using in English for the word Love?  They refer to different kinds of love, which we can not directly express in English.