Did it in 2014, first week of June.
Both Transalpina and Transfagarason were officially still closed but many ppl (cars + motorcycles) ignored that and did it anyway)
pdvsecondblog: Transfagarasan in pictures

There was still a whiff of snow at the top of TFGS, but it was do-able.

I would just go, and ask locally.
But be prepared to turn around if you hit real obstacles.
The whole area is Nice, so you will enjoy anyway.
But the Valley from Ramnicu Valcea to Sibiu can be a bit congested, even on early Mornings.

Edit: I notice you want to go London to Istanbul.
On that Balkan-part (Romania / Bulgaria), and especially if the weather (or forecast) for Carpatians is snow:
you might try to follow the Danube valley from Belgrade to Djerdap and cross into Romania.
Google: Iron Gates, a very nice ride, did it in 2017,
documented here : https://myadventure.bike/Trips/390 - you need to zoom in.

I read you like to "push the bike" but just in case you get tired:
the Bulgarian mountains are slightly lower (less snow) and have generally (much) better quality roads (Google : Freedom Arc, Shipka pass, Buzludzha, or further south: Rila, Bansko, Sandanski, Gotse Delchev, soo many nice places. If you find him you can even go visit Graham Field, he lives on a beautiful hillside down in Bg when he is not on the road)

Edit2:
I'll be in Borovets (S of Sofia) on 6-10June, and in Bucharest on 12June myself.
I might re-do some of those roads if time permits.
And there is a place called moto-camp just East of Veliko Tarnovo where HU had a rally once. Noteworthy and Recommended.

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