Well, I've got that out of the way for now, so here are some tips and recommendations from me:
Government's own guide to benefit appeals is quite useful (plus you'll need it to start your appeal anyway):
https://www.gov.uk/appeal-benefit-decision
The DWP produces assessment guides:
Part 1 goes into detail about how the Health Professional should conduct the assessment - you may be able to make a case if you can prove that it was not conducted in accordance with the guidelines.
Part 2 gives the assessment criteria in detail, and indicates how many points you should be awarded for each descriptor.
The AdviceNow website has a mandatory reconsideration letter generation tool which can also be adapted for the appeal stage:
https://www.advicenow.org.uk/pip-tool
It also produces a PDF document entitled "How to win a PIP appeal", which contains worked examples.
Have just seen that AgeUk can possibly provide advice on this: caree just about qualifies, I think

Otherwise, my locality seems to be short on people who can advise about appeals, and the CAB hasn't got back to me yet wrt my request for advice.
The Benefits and Work website (forum and publications) has been very helpful:
www.benefitsandwork.co.uk
It does cost nearly £20 for a year's subscription, but I'd guess it's likely to be worth the investment in most cases.
Publications (free to members) include Best Possible PIP Appeal Submissions (one of the worked examples being a sufferer from ME/CFS); Best Possible Ways to Challenge a PIP Medical Report (grounds of appeal with sample texts); a CFS diary template, etc.
The forum is also particularly useful, although you should be aware that your posts will, initially at least, be moderated, and that the moderators are only available for a few hours, and not every day, so it may take time for your posts - and answers to them - to appear online.
I didn't find the Turn2Us.org.uk website particularly helpful, nor the MEAssociation one.
Hope this will be of benefit to someone else, too!