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Your choices are extremely limited - Shoot either a 50 or 55 grn Burger. The later of these bullets drill straight through rabbits and foxes, the 50 grn may be better ??.
I don't know how either perform of deer. But I do know you will need a custom barrel fitted with the appropriate twist to stabilise these pills.
The bullets WILL be harder to source and cannot be posted as they are classed as expanding ammunition. Plus they will be far more expensive.
and after all that - you will still have a rifle that is far less versatile and suitable for deer than the 223 or any of the 6mm calibres.
Is it any wonder why the bullet manufactures don't produce a 204 bullet meant for anything other than small vermin. But its your money and your choice..... So good luck with that
Just for accuracy - regarding your post - the 204 has "far more energy than .223" IT DOES NOT.
example. 223 shooting a 53 grn Vmax generates 1413 FPE - The 204 shooting a 40 grn Vmax generates 1351 FPE .
They are factory figures from Hornady
Have fun whittling your 0.224 bullets to 204 cal - I am sure they will be very accurate.
ATB
Alan