Yes, it's possible to change. No, you will not be able to do it for free. And no, it will probably not be any different if you ask in person.
As Paul notes in his comment, your previous experience is not analogous in any way to your current one. Delta is not whatever airline you flew before; it has its own rules. Moreover, it sounds like you are flying as an ordinary revenue space-positive passenger, not as staff. If you were deadheading before, you had priority so that you could be positioned properly and so the airline's operations would not be interrupted. If you were flying nonrev, you were already flying standby, and simply lucky that seats were available on the desired flight (as you note, it was practically empty, which will not be the case for any domestic flight in the U.S. this time of year).
Whether or not you can change a ticket and what the associated costs would be are governed principally by two things you agreed to when you purchased the ticket: the airline's contract of carriage (or conditions of carriage) and the rules of the fare you purchased.
The fare rules are likely to indicate the amount of the change fee, which is currrently $200 for domestic Delta-marketed flights, and what the bewildering rebooking rules are for it— whether your new ticket will be charged at the current or original price for the fare class, whether the change fee applies to the ticket or to the sector, whether any refund must be used immediately, and so on and so forth. For discount economy tickets, the rules often mean that if you require a change, the value of the ticket is essentially forfeit, as you have discovered.
The rules are furthermore programmed into the airline's reservations systems, and on a simple change like this, I would wager the airline agent will see no differently from the website. Even if you could find an agent who was sympathetic and had sufficient access to override those rules, that change would be recorded and the agent would need to answer for the change.
To be clear, merely wanting to leave two days early is never an adequate reason for a free change, so barring extraordinary events— say, a hurricane is making landfall on the day you are scheduled to leave, so the airline issues a blanket policy allowing free changes to depart earlier— what you want is not realistically possible without paying extra. Next time, you'll have to buy a flexible ticket (which costs substantially more) or try to find an airline with lower or no change fees (which may not fly where and when you need them to).