Hi Adrian,
Thanks for your advice. Your first suggestion sounds like it's an easy option.
I tried using your Migrator module and I think it worked for the most part - it changed the admin URL from what I had originally which threw me for a bit because I was getting 404s, but I soon worked that out. The only other issue I noticed was that the restored profile included your admin user account but that wouldn't be hard to fix.
I think it's probably best for me to just do a new install from scratch and choose the blank profile. I've found that using Softaculous to install ProcessWire also gives me the wrong timezone setting so fixing that and the profile issue would probably take longer than doing a "normal" PW installation, so I think in future I won't bother with Softaculous.
Thanks again for the suggestions.