Hi
The option of using either Braithwaite Fold or Rayrigg for your first night is probably the best plan if not ideal.
These car parks are operated by South Lakeland District Council who have wisely opened up the option of overnight stops.
I can offer the following comments based upon my location, current participation in managing visitors to the LDNP and as a qualified mountain leader based in the lakes.
All 'fly camping, camper van and great white activity is monitored every night by the multi agency patrols. After a horrendous summer in 2020 the N Park and other stakeholder agencies were on the front foot for 2021. The aim is to provide a good visitor experience; 'what you can do'. The message is 'leave no trace..' All known 'fly camping' locations are visited each day/night by one of the multi agency patrols to ensure compliance with regulations and landowners wishes. Martindale was gridlocked last weekend, as was most of the lakes.
Glenridding Car Park will be on 'Amber' by 08.30 and 'red's (full) by 09.00. Refer ro Saferlakes at Lakedisrict.gov.uk for up to minute information on car park availability. My tactic is to be parked by 07.00 or 07.30 and get going. On a route like Striding Edge you will probably have other people with you, but very few compared to the procession of ants that complete the traverse later in the day. In the car park i try to get a space parallel to the kerb on the ramp between lower and upper sections; avoid the trees at all costs as the birds will bomb you with white stuff! If you start early then the flesh pots are all open on your return (and incredibly busy and slow due to a County wide staffing crisis) and you will have time to visit and arrange a campsite in the afternoon.
Lake District National Park policy is that people do come and enjoy their park...appropriately. You will meet volunteer Visitor Support people on duty in all big car parks and hot spots. They have up to minute briefings from Safer Lakes and the Multi Agency response teams via WhatsApp. Visitor Support presence is so that the public can talk to a knowledgeable local person about activities, facilities and alternatives.
No apology about the length here. A week last Sunday saw the busiest every day in the Lakes. Valleys in grid lock, no car parking whatsoever in Central and fringe lakes, accidents and a tiny proportion of unfortunate behaviour and activity. The Park is being overwhelmed currently; staff and volunteers are present to welcome and help. However, the infrastructure has nothing like the capacity for current demand.
Start nice and early, have a great day, and stay safe.