Here is a past map of the event site and the surrounding closure. If the past is any indicator of future conditions the closure will be very much like this.
From this map I see that entrance to the eastern side of the playa is unrestricted as far as the Burning Man closure. So entering the playa is a go from the east side. Then the decision is how to gain access to the event. The event has entry points for participants at the gate and the airport. Airport is questionable and gate is probably the best low hassle approach.
If it were up to me to chose a route to entry I would travel well outside of the event fence on the southern edge. Once I had gone far enough that gate was at my 1:30 I would turn to intercept gate road about 1/4 mile from gate to make it around the western edge of the sprawling gate complex.
I think it will be nearly inevitable that you will be intercepted by either LEO or Perimeter. Following their commands/advice may be necessary. I hope you run in to someone who wants to be constructive rather than the opposite.
I think the playa portion of the trip holds a fairly high danger from all the extremely high speed vehicular traffic I have seen there. Having a tall flag may help overcome some of the mirage effect that seems to obscure things that are close to the ground.
Best of luck with the trip. It sounds like a great adventure.
Motz speaks true, as well.
Just know, as he says, Perimeter will have seen you before you enter the closure area.
Try to stay out of it.
and, if you're going to cross, find the shortest route, and hope, you get a kind intercept. Attitude can easily determine this.
And, hope intercept is by GPE personnel. Others are not always as helpful, or willing.
On that south side, you'll also be dealing with the airport.....and, it's even more important to keep slow moving vehicles/people well clear of the runway, and a fair area around.
You might make sure you have a tow strap.....in case an offer to tow you across faster happens.
Also, the playa surface, as you well know, can be very unpredictable, and, I've seen it very soft and full of dunes in that area. Tough pedaling for sure.
It seems it'll be a fine balance, between direct route to gate road, and, impending intercept, by the adept, astute, articulate and disarmingly sexy GPE folks........and pray not to get popped by LEO or BLM........they're not nearly as good looking.