Thanks to Elmo for pointing out the Bad Elf GPS loggers here:
bad-elf.com/pages/compareUnfortunately, the lowest cost two have the MTK GPS chipsets in them and so do not log the accuracy data.
The their one however, called the 'Bad Elf GNSS Survey' has the U-Blox Neo7p GPS chipset in it and is capable of logging the data we need at up to 10z. It seems to have enough memory space to log for over 24 hours and a battery to match that.
The biggest catch with it is the price at US$599! That makes it about A$850! Far too much for most I imagine, especially as you would still need two units for records.
I have contacted the company to see what they can do for us. I will post updates as I find out.