I'm in South West UK.
If you stood a UK Sika next to a UK roe, there'd be no confusing the two -don't know how large/heavy your US sika are, but I agree that your trophies do look surprisingly similar to my buck photos.
In UK, roe antler span varies significantly over short (eg 50 mile) distances.
As I said, I'm in the SW. Here, spans are quite wide -contrast my 1st photo with 1894's 2nd- his beast has a much narrower span (but is nevertheless very heavy - 1894- a gold?!)and (I think you'd agree) looks less similar to your trophies. I dare say 1894 is in a different part of UK to me (1894 -South East?).
I'm sure if we were able to put the two side by side, your sika heads would be noticeably larger.
Hereís a photo of a well proportioned (but non-medal) head, Iíve put a ruler next to it for scale, I guess it will measure much smaller than your heads: