H'm, sorry Braveduck - I've not got a definitive answer to hand - but I've seen it online somewhere recently. (From memory, no, I don't think the fill is shallow anywhere - the real floor of the chamber is a long way down all over.)
In case it helps, a caver called Bill Spencer who died a few years ago made a lifelong study of the floor of the chamber and how the sinks and sediments are different between flood events. I'm pretty sure Bill's interest in this stemmed from his involvement in recovering the body in 1947. In the latter part of his life he wrote an article in a CPC publication entirely devoted to changes in the sediment floor of the chamber which is somewhere in a CPC publication (probably "Record" rather than "Journal"). I'm a bit too pre-occupied with another job to look this up for you as I type but there are various indexes available to CPC stuff (at least one online) - or someone else might kindly post here where this can be found.
(If you are absolutely desperate to have the definitive answer on the GPR work then PM me and I might be able to put you in touch with someone who was directly involved.)