tens of thousands of arched over white birches.

[Nemus Talea]

I agree, "cut like heavy leaner" but be ready to move. Shaped in an arc, small branches will touch ground with weight coming from above with final cut. Energy will load in those branches and create a potential for butt end to shoot back. May also roll and give a kiss as ya retreat at angle.
For most situations it would probably be best to dump over at right angle to lean. I don't see much birch bent like that so not sure if a baby barber chair would pop out as wood is cut to hinge width. Take care that your head and neck are away from possible path.
A pole saw could allow more aggressive and productive work while having a safe distance.
The little guys can git ya bad. As always,take care.

 

[Nemus Talea]

If I had to clear a whole grove of those things I'd want pole saw. Flop em all to one side then gather in grapple.

 

[Philbert]

For most situations it would probably be best to dump over at right angle to lean.

I like this option. Not one I would have thought of right away! Mind gets stuck in an 'either/or' frame.

Thanks.

Philbert