Transformer Design Using AP Method and Construction
Too long for a comment but not really an answer...

I would observe that the core loss vs flux density curves plotted on P.2 of the Metglas document cover the range 0.05 to 0.3Tesla despite the saturation flux density being quoted as 1.56T on page 1. 

This is a pretty good hint that the expected range of operation is within that flux density range.

I don't know how you've calculated core loss at 0.6T and 1T but if you used the formula on that graph I'd caution against extrapolating it to flux densities outside that range - or even using the core outside that range at all - without explicitly talking to the supplier's application engineers and gaining their approval for what you're doing.

That formula is clearly an approximation (anything with a power of 1.74 is a "best fit" from plotted results not a physically realistic formula!). 

So, given that it's an approximation of a non-linear phenomenon, you can expect unpleasant surprises if you apply it outside its applicable range.

As far as cooling is concerned ... if you are dissipating 1.3kw in this core, you can't expect to remove that heat by simply bolting one side of it to a heatsink, without knowing and modeling its thermal conductivity - or thermal resistance - neither of which I can find in the data so far - nor do we know the physical dimensions.

We do know the saturation flux density decreases with temperature (to 1.1T at 300C) and the Curie temperature is 399C. I can see thermal runaway leading to hard saturation. So operating at a flux density of 1T looks like a bad idea in any case. 

Given a model of its thermal resistance you can model the resulting temperature increase resulting from core loss - and decide on an acceptable level of core loss to meet a realistic temperature.

I will freely admit to being out of my depth at these power levels and only scraping the surface of these issues. But they are real issues. And I'll repeat my suggestion to talk to the FAE. 

But my guess is that you'll have to redesign for the manufacturer's recommended range of flux densities, which will probably reduce the core loss to something closer to the copper loss for a more efficient design. That will in turn reduce the cooling requirements and the problems resulting from temperature increase.