Unfortunately, ICSID won't reimburse for "lost profits"( only cost)

That is an unsound statement, do you have any substantial legal support for it?

It is not clear what the arbitrators would award, particularly in light of the BIT requiring that, "[s]uch compensation shall be based on the genuine value of the investment."

Few BITs have such a clause and thus are not relevant.

In essence, while I doubt we go to arbitration, I believe that far more than sunk costs are available. I've actually done international arbitration and understand the process and the latitude of the arbitrators, do you?