There isn't really a magic bullet to solving the compression / knock issue. Adding a point of compression gives a few percent thermal efficiency, but unless you can run Atkinson cycle, you then lose that efficiency through retarding ignition timing, or you lose the monetary gains through high octane fuel. Turbos are just another way to get more compression, and come with the same set of issues. There are combustion chamber tricks, such as Logic's quoted tuned headers, changes to piston design or valve timing or combustion chamber shape, but these are largely outside of our control as lay people.
I'd wager the best engine swap might be one of the Toyota Dynamic Force engines. Honda never mated their highest efficiency engines to a manual transmission; the L series in Honda's hybrids were 13.5:1 CR in the automatics, but only 11:1 in the manuals. Mazda did Atkinson Cycle + manuals right, but due to cheaping out on materials, their efficiency is only mid 30's %, similar to the non-Atkinson Honda engines. A Toyota 3- or 4-pot Dynamic Force engine can reach 40-41%, they have manual transmissions available, and make decent power. Nobody else, other than perhaps Mercedes, seems to be building maximum efficiency gasoline engines.
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