The only fretsaw I know of that is capable of cutting wood up to 5" thick is the Diamond... which would struggle... and is now only available second hand

. My advice would be to get a good band saw and if you have to make piercing cuts,make them manually with a bow saw. If you don't fancy learning to use a bow saw, make a template for your pierced work and rout it with progressively deeper cuts from a router fitted with a template following cutter and a shaft extension.
And rout it very, very carefully. It would be wise to take out a lucrative insurance policy beforehand.
Gill
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