Yeah - it's not really (0.5A + 2A)/2, it's (0.5A1 + 2A2)/2, where A1=2*X (as you have above) and A2=X. Substituting, your expected value upon changing is 3X/2,

Yeah - it's not really (0.5A + 2A)/2, it's (0.5A1 + 2A2)/2, where A1=2*X (as you have above) and A2=X. Substituting, your expected value upon changing is 3X/2, which is, surprise surprise, the same as the expected value for the envelope you already have.