If you reread through this thread, you will note that I offered multiple alternatives.
And I spent considerable time doing so.
It does appear, however, that I did not offer the solution you kept asking for.
That is - "Well, if you can't find a campsite, then go ahead and stealth camp."
Others suggested as much.

Bike touring is one of the most privileged activities - esp. multi-month, epic tours.
I am beyond fortunate to have done many - - as are you.
The vast majority of people in North America, let alone the world, do not have the time & money.
And so - no - heavily-used parks are under no obligation to make special arrangements for cyclists.
It is a generous special accommodation where it is available.

I have toured the Canadian national parks in the Rockies a half dozen times.
From the U.S. / Canadian border to 60 degrees north and further.
Not once have I been stranded or had to go off into the woods in the parks.
Nor would I ever do so. Because to do so simply adds to the ongoing human impact.

We are witnessing one of the greatest mass extinctions in the history of the planet.
If that means that I can't do everything I want to - when I want to -
in some of the few remaining wild places, places that already have high human impacts,
then I am more than o.k. with that.

And if that sounds "preachy" - then so be it.