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Ironclad I don't think he's going after Eliza just yet. Remember that as far as he knows, getting involved with Eliza resulted in a "bad end". While he likes her per se, her personality was a major turn-off.
Obviously though, he's made major changes to "his character" and he's undoubtedly set on a far different path than the mob character would have. Probably had he not remembered his past life, he would have stayed fat and watched his domain collapse. But now he's made major changes, is working hard to see his domain turn things around, etc. Definitely he's aware of Eliza's shortcomings and we're likely to continue seeing flags where he tries to get her to face herself and make friends with his merry collection of people.