You can change for free, so long as you're keeping the same origin and destination, and you did not previously accept the schedule change.

Now, CO agents will often accept the schedule change in the system, so that even if you do not agree with the new schedule, the computer will show that you did. You may first need to prove that, especially since you already talked to an agent. It is very likely he/she "accepted" the change for you already.

The agent's response is typical of CO -- basically trying to get more money out of you. You need to counter with the proper terms.

"There is no change fee due to the schedule change."
"They should not be charging an add-collect because this is an involuntary change."

They will likely give you nonsense like "Your fare class is not available on the other flights," or "I can waive the change fee but not the fare difference."

To which you will need to reply:

"That is not correct. The fare class can be overriden since this change is involuntary," or
"I'm not asking you to refare the ticket, I'm asking you honor the original ticket on those flights at no additional cost. Can you do that, or maybe is a supervisor needed do that?"

Basically keep repeating yourself and escalating til you get what you're entitled to.

If they say something like, "Then all I can give you is the flights the computer put you on," you will need to counter with "I do not accept the schedule change."

After a few rounds of this, CO will likely try to offer you a refund. To that, you will need to counter that you're not interested in a refund, you're asking to CO to honor your ticket with the flights you request (if your case is that the new flights you want are nearest your schedule, use that).

CO has a history of being nasty with schedule changes, so good luck!