Did you ask when you got to LAX if you could go standby on the earlier flight? Telephone reservation agents are bound to the rules and most changes will incur a fee and possibly additional fare unless you buy an unrestricted ticket or travel on an airline without change fees like Southwest, but even they charge for fare differences. Agents at the airport have more leeway especially if you are already at your connecting point and want to go on an earlier flight. Sometimes there is a same-day change fee of $25 - $50 dollars but sometimes if you ask nicely (and the agent is in a good mood) they will get you on at no additional charge.
The reason for the differnce in price was that you were looking at the one-way fare from LAX to Santa Barabara. When you called to make the change the agent you were speaking with was pricing the ticket from JFK to Santa Barbara which is a completely different fare. Even though the portion of the flight you were looking to change was the same origin and destination when priced using JFK as the origin there may have been a larger difference due to availability. Fares and availability are dynamic and can change from minute to minute.
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