Hi,
As July is more popular for a trip to Trinity buoy wharf, how about another possible set of dates, how does the 10th/11th of July work as an option?
So the likely dates are
Saturday 3rd July
Sunday 4th July
Saturday 10th July
Sunday 11th July.
I suspect 2-3 hours would be more than enough here, including a refreshment break, which would be a nice outdoor social gathering, there is a 1940's diner and an outdoor bar on site, with London prices!
Parking appears a bit limited , in Orchard place, under the pink line. There don't appear to be restrictions at weekends (looking on Google street view).
The yellow square is the outline area of Trinity buoy wharf.

The pink line is the walking route from Canning Town DLR/Underground station, it's 1.2 miles each way.
The purple line is a detour to go to the Eco park.
The flesh colour items show the driving route via A13/Blackwall tunnel. At weekends, it is quite busy from mid-morning, today there were 15 minute delays.
Last time I used the DLR, I drove to Woolwich, parked my car and a trip from Woolwich to Canning Town will be £1.60 each way. On a Sunday, you can park at Woolwich Arsenal Station for £1 and it is £4.30 for a Saturday. This avoids the pain of Blackwall Tunnel.
Pick your potential dates, the majority wins and I'll add it to the Calendar