Judy
I think it would help if you told us what you have actually verified about 'your' Frederick - the stuff you have hard evidence for such as birth cert, parents, address on the cert etc. Also if you have birth certs for Frederick (1920) and siblings - I know nothing about US birth certs, but there must be similar info on them to british.
I am confused about the place(s) of birth - the attestation papers say Gwenepp, then you seem to think Calstock - these two are quite a way apart with Calstock being very close to Devon. Incidentally if you are relying on the IGI entry for Frederick William Cardell Pengelly then you should be aware this is a member submitted entry, rather than an extraction - not to be relied on, I think most would agree
I have done a quick search of IGI/BMD and there seem to be many Frederick Pengellys in the area. Obviously you have some information regarding earlier family as you mention a Carkeek connection - that may help.
Ok - I've no found this, which appears to be your Fred
1901
Frederick Cardell Pengelly b 1861 Chasewater, Cornwall Head Gwennap
Elizabeth Jane Pengelly b1869 Gwennap, Cornwall Wife Gwennap
Frederick Carkeek Pengelly b 1893 Calstock, Cornwall, Son Gwennap
Gwendoline May Pengelly b 1897 St Day, Cornwall, Dau Gwennap
Elizabeth Myra Pengelly b 1900 St Day, Cornwall Dau Gwennap
RG13/2238 f50 p15
RD Redruth
Sub-RD Gwennap
ED 5
BUT
I have also found this
William J Pengelly b 1869 Calstock, Cornwall Head Calstock Cornwall
Sarah J Pengelly b 1873 Calstock, Cornwall Wife Calstock Cornwall
Frederick W Pengelly b 1893 Calstock, Cornwall Son Calstock Cornwall
William J Pengelly b1896 Calstock, Cornwall Son Calstock Cornwall
Lilian B Pengelly b 1898 Calstock, Cornwall Dau Calstock Cornwall
Russel C Pengelly b 1900 Calstock, Cornwall Son Calstock Cornwall
RG13/2115 f111 p42
RD Tavistock
Sub-RD Calstock
ED 6
I think the second one was possibly the Titanic passenger.....