As you note the heater core needs to be replaced. The cost is mainly due to the labour, so you could shop around for a lower estimate, but it is not likely to be significantly lower.
An alternative is to buy a radiator sealant for the cooling system. It is usually effective for minor cracks which yours sounds like. It is not expensive, but you must follow the manufacturers directions. It will take a few trips to circulate through the cooling system and seal the leak. Do not be disappointed in early lack of results. In my experience it works and will last for a while.
Hope this helps.
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Art
2000 Taurus SEL Wagon 3.0 Vulcan (daily driver)
1993 Taurus GL Wagon 3.8 Essex
1991 Mercury Grand Marquis LS 5.0
1986 Chevrolet 3/4 ton pickup 4x4 350 with turbo400 and 208 transfer case
1978 Chevrolet 3/4 ton pickup 4x4 custom 6.2 na diesel with turbo400 and 203 transfer case
Planning 2008 Taurus X in a year
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