If you share it some other people might take a look. I would bookmark it to look like a week from now and see if no one else has. High order RK methods are just not stable and not a great idea for PDEs, so Vern7 would be one of the last methods I would check here. CVODE_BDF(linear_solver = :GMRES) might be a very easy way to take a chunk off, or ROCK4().
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