Planar headphones

HiFi Man is a good choice for a magnetic planar headset. Available for around $500. I wouldn't spend more!

I was wondering if a pair of planar headphones comes close to the sound signature of a planar speakers, I’m looking at a pair of headphones in the $1000 range.

No.  In my experience headphones are just a totally different experience than listening to speakers regardless of the technology.  That said, I really like my Hifiman Arya Stealths that are now available right in your price range…

https://store.hifiman.com/index.php/arya.html?utm_source=storewebsite&utm_medium=landingpage&utm_campaign=BTS20230804

If you can stretch to the HE1000 Stealths at $1399 (also on sale now) I think it’d be an extra $400 well spent.  Of course you’re gonna need a good headphone amp to get the most outta either of these if you don’t already have one.  Hope this helps, and best of luck. 

To your question, simple answer, no.

I think it might help to know what you consider to be the sound of planar speakers. I have both planar speakers and headphones and I don’t find that the sound of the planar speakers translates into anything that I hear on my planar headphones. The sound of the speakers is heavily dependent on your room and set up. Not so much for the headphones, if at all (but your choice of a HP amp can make a big sonic difference). FWIW, my room is not optimum for planers, or electrostatics, speakers for that reason I have (as you) forward firing boxes. I haven’t heard all of the available planer headphones so I don’t know how much of that design adds to their sonic value, but found prefer good quality 'ordinary' headphones. And I think this preference is base on, as much as anything else, synergy and the choice of the amp.

I don't think so; I've got separate systems for 2-channel and for headphones, and speakers and headphones are just not comparable - one is not 'better' than the other, just totally different experiences..