Am I able to transfer all my hours to a new logbook, and get a CFI or similar to sign it off, confirming via my old logbooks that all is present and correct?
Yes, just bring all totals forward to a new logbook.
No-one needs to countersign the transfer except you. But keep your old logbooks for 2 years or if needed for licence issue, whichever is the longer.
Anyone tempted to 'inflate' their totals should note that the CAA will take a
very dim view, should they be caught.