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PA3041, the quickest way here would be to find a real power electronics engineer in your area and ask him/her to measure the Lmag, Llk, and coupling coefficients of the Tx, also the Rac, RDC of the pri and sec,
also the self res freq for pri and sec ( SRF ) - then it may be possible for that person or a gifted engineer on this forum - or elsewhere - to design essentially the same transformer on a gapped long E core with a split bobbin - with litz wire to get close to picture number one in performance ...