I have had this exact issue and I just got it solved...It was the ignition switch. I replaced the ignition switch and that fixed it. At Honda this is $106 for the part and 1 hour of labor...I was out the door for $153.
I replaced the main relay about a month before and it apparently did something to help the problem, but I was dreaming...The old ignition the technician pulled out he handed to me adn it was fried...The solder point was completely melted and the ignition plastics were discolored throughout like it was about to, or already had, been charred by electricity way too many times. The van has 212k, probably 200k starts...that is enough to fry anything electical.
I thought about trying it myself, it looks very easy, but there are two bolts that are "safety bolts" to uninstall and re-install the ignition (translation: Honda does not want anyone but the dealership to work on their cars..).
The tops of these bolts are sheared off at the factory after installing it so the car cannot be "stolen".... Again, I am pretty sure they just don't want me to fix it myself. So I went with the Honda technician on this one since I didn't want to mess with those "safety bolts". He did show them to me and they are for real. The average person would have to get in there and most likely drill them out in a very small space. I just wanted the thing to run so I ponied out the 150...