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My suggestion with Amazon price.
5D Mark III $3499
Canon 24-70L $1769, I think you can wait 24-70L II, it will be in stock this year.
Tamron 28-300mm f/3.5-6.3 VC for Canon $629, It is...

Just do it, 17-55 IS is the most valuable lens for Canon APS-C cameras.

I agree with your point 70-200mm f/4L is sharper than both the two 70-300, and AF, vignetting, and distortion are actually a problem.

But If I need IS/VC feature, and the money is limited, what...

Through the ISO-12233 sample image, I thought 'EF 70-300 IS USM' is much more blur than A005 at 300mm. The mid frame and corner is very worse than A005, and the center is very similar.

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