Conjecture: Let s be a winning E-strategy for phi. Extend s to s' by augmenting the tree wherever required so that the result is a winning D-strategy. Claim: The E-violating moves will occur after P has asserted an atom.
Check back often for evidence for or against this conjecture.
The second one is one that Chris proposed, namely whether D10+D12+D13=CL (i.e., we drop E, but add D12). Now, you might recall from a week or two ago that I conjectured that D10+D12+D13=IL, not CL (and I already have an easy proof that D10+D11+D13=IL), so it will be interesting to see how this pans out.