I've never managed to find where my ancestors are buried either but I think in the main they were a poor lot and so may not have marked graves.
An email to Swandean may produce some results so it is a step in the right direction.
However, with difficulty

I navigated the website for West Sussex Records Office, since TNA say they have some Swandean Hospital records there....
and what I found was:-
Catalogue no Ada MSS 29224
Title: Register of patients admitted to Swandean Isolation Hospital from areas outside the Borough of Worthing. July 1938-June 1948.
Description: This register records the name and address of the patient, authority from whom transferred, disease, date of admittance, date of discharge.
This information can only be consulted with the permission of the County Archivist and is not available to the public for 100 years.
I would have thought that if you email or telephone them they may be able to pass the information on to you as you are a direct descendant.
I do hope you have success. At least then you may know what happened to his body and then you can work out what to do next.
There is also information in The London Gazette about the solicitors acting for Eliza Kelway Bamber, after her death. It looks as though you could get her Will if you're interested.
Good luck and do tell us how you get on
