A little follow-up on VTTA: due to recent changes made to VTTA by its creator (Sebastian), I was experiencing more and more bugs and having increasing difficulty using D&D Beyond with FVTT.
(As proof of this, the VTTA D&D Beyond Integration given in this post is broken…)
Then I discovered D&D Beyond Importer by MrPrimate (thanks to Matt @encounterlibrary) and it now works like a charm! 
NB: all useful links (including an excellent module overview by @encounterlibrary) can be found on the module page.
Edit : just read this post from @kakaroto announcing that The Forge will soon provide a D&DB integration service of its own, which will be available to his patrons…War is raging between FVTT developers! 