"IRS replied that you can not use the amount of the exclusion when figuring EIC"

In Phase 1 training, they teach that unemployment is not earned income.  Call back next month and they will know from Phase 2 that if the exclusion reduces AGI to an amount that allows EIC, the "automatic" IRS amendment will not compute it -- you still have to file an amended return, as pointed out by @Just-Lisa-Now-  above.