Check your ram usage before and during the transfer. If that checks out, you might want to either try transferring in smaller batches (which can get annoying) or submitting a bug report on it. If you need help with the latter, reach out and I'll do my best to walk you through the process

The memory usage looks ok; I have 16GB and 12.75GB is being used. Whilst the transfer process is running, Thunderbird is using 900MB and I've seen this go up to 1GB.

The process appears to stop when I'm not using the computer for a while and the lock screen is activated. I set the transfer running yesterday and continued to use the computer for several hours and the process continued with no issues, so cause appears to be when there is a period of inactivity. I assume this process should continue to run despite me not being active on the system? I'm not sure if this is an issue with Thunderbird or how macOS works?

Try using a filter. Create a filter with the criteria for the messages you wish to move - a date range for example. Then run it on the folder that contains the source message. It will be slower but far more likely to succeed.