I would prefer May or June. July & August would be too busy with Schools off and too warm for cycling. September is a good month, June is favourable due to the longer daylight hours and climate is more comfortable.
Another factor to consider is the cost. I know this has been discussed before. I could on and on, because it's a big project to take on. Still plenty of time to work things out.
One idea is these who want to do LeJog is to meet up a for Week-End at a Youth Hostel @ Edmundbyers. Do a ride around there and then a drink afterwards in the Punch Bowl to talk things over.
If a start was from Sunderland Rail Station to Waskerley Cafe (004432)
That would be 35 miles and ascent of 2968' which is sea-level to 1312'. The Youth Hostel @ Edmundbyers is 5 miles from the Cafe with a descent of 850'
P.S. I take the Waskerley Cafe is the one at Parkhead that is run by Lorraine Turnbull (ex Sustrans)