John 6:38? Allow me to first say, that I do not believe John 6:39 and John 6:40 are speaking of identical things (as though the writer is simply repeating a truth twice, here). I believe verse 39 is speaking of something distinct from verse 40 (though not wholly unrelated). Verse 40 is speaking of "persons"... whereas v.39 is speaking of "things" (so to speak) which were given Him (such as "government/governance/rule" etc...)
The context indicates otherwise.
Besides, John 6:44 says this:
John 6:44 No one can come to me unless the Father who sent me draws him. And I will raise him up on the last day (ESV)
This is talking about a resurrection to glory. In other words, all the Father draws will be raised up in glory.
Additionally, if you read the entire chapter, there are multiple statements concerning the chain of redemption that don't allow for the possibility of failure.
Regarding the other verse, there's no contradiction between Reformed theology and "everyone who believes" or "whosoever believes" in Reformed theology.
The teaching of Reformed theology is that God regenerates sinners, changing their nature, leading to faith and repentance.
Therefore, anyone who brings up John 3:16 or similar verses in response to Reformed theology isn't really responding with anything meaningful since the real issue is, what creates belief? Of course, the Reformed person believes that everyone who responds in faith and repentance will receive eternal life, because only the elect will respond in faith and repentance due to the changed nature.
For the free-willer, faith and repentance is something self-manufactured, and under the control of the person. For the Reformed person, it is a result of the regenerative power of the Holy Spirit.
For the free-willer, you exercise faith and repentance in order to receive a new nature that wants to please and love God. For the Reformed believer, God regenerates and changes your nature to want to please and love God, and the response is faith and repentance.
This is needed due to the fallen, corrupted nature that is a result of the Fall.
Decisional regeneration (regeneration as a result of a decision made by a corrupted man rather than something God does) is really backwards, and it also offers individuals reasons to glory in their own merits.
Spiritual troglodytes hate the light, and that's exactly what unbelievers are:
John 3:19-21 19 And this is the judgment: the light has come into the world, and people loved the darkness rather than the light because their works were evil. 20 For everyone who does wicked things hates the light and does not come to the light, lest his works should be exposed. 21 But whoever does what is true comes to the light, so that it may be clearly seen that his works have been carried out in God.” (ESV)