Question

Does Gita support doctrine of eternal samsara?

Answer

Samsara = bhumi + svarga + naraka

Samsara is eternal. Creation and Destruction have always happened and will always happen. 'yatha purvam akalpayat' - RigVeda 10.190.3

Krishna says :

I forever punish evil men

You interpreted :

I punish evil men forever

Krishna says :

Evil men never reach me

You interpreted :

Evil men never reach me

Good or Evil are characteristics of an action, not of a person.

If a person does a good action, we 'temporarily' label him as good person.
If a person does a evil action, we 'temporarily' label him as evil person.

You're wrongly assuming that once a person is labeled Good or Evil, they remain that way forever. That's not necessarily true. Because after they finish facing consequences of action, the person goes back to blank slate (kind of, cos vasanas of action still exist, and these powerful vasanas propel you to do same acts as before).

Bhagavan does not damn sinners to hell forever.
Bhagavan does not deign saints to heaven forever.

Both are temporary. After exhaustion of the rewards or punishments, the Jiva has to return to earth. 'kshine punye martya lokam vishanti' - Bhagavad Gita 9.21

Since Samsara is eternal, there will always be saints, sinners and normal people.
As long as sinners exists, Krishna will do his duty of punishing them. Duration of punishment depends on type of sin.

The Jiva, out of his own free-will, can choose to stay in samsara, or get out. But only the will is free, the consequences are not. That is in Bhagavan's hands.
Where he stays within samsara, what happens to him during his stay, and how long he stays, is a combination of his free-will to act, and Bhagavan's free-will to react.

The whole point of Bhagavan using such harsh words in Gita is to drive home this point :

A person, as long as he does evil acts, cannot reach Me.

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