Normally I'd say "none", 3rd person is fairly easy, easier than 1st, so you should be fine but...
You're rewriting into a 3rd person partially omniscent with access to two minds. Ouch. Ouch again.
That's what I tried to do just recently, thinking "It will be fine". It backfired. It's neither a proper omniscent, nor a proper partially omniscent. I was confused writing, unable to find myself in any proper perspective; I don't even want to think of the reader. I ended up scrapping the "double partially omniscent" and went with classic "single-user partially omniscent," switching whose head he's in each scene. That got somewhat less awkward but I'm still pondering switching to 1st person because while that works for me I still don't know if the perspective switches will be clear enough for the reader.
Maybe you can make the "Dual head" work. I couldn't, it's such an unorthodox perspective, I just can't place myself in perspective of observer of two minds at the same time, and I'm pretty sure neither can my readers.
Your first other option is go for behaviorist/"flying invisible camera". Give up the "omniscent" part altogether, describe reactions and gestures but never feelings or thoughts. That's an impartial report, a clear solid perspective if done properly - but it requires a good deal of mastery to convey it all, not to come out dry and sketchy or confuse with misunderstood emotes.
Your second other option is to go all out full omniscent. A.K.A. the cheesy one. Easiest to write but hardly immersive, "tell, don't show", with a big "Novice writer" neon sign blinking on top. Do I have to elaborate?
And your third other option is to give a finger to your agent, give them their 3rd and cheat them by bracketing the whole thing into a retrospection. Pick a nice flat "behaviorist" 3rd person, seat the two protagonist in a nice cozy room with a willing audience, and have them weave the tale together, each in their own 1st person, with the meta/main/bracketing level serving an extra function of added flavor, as they argue about points that they still didn't agree on, or correct each other "augmenting their reality" or throw in other "meta" notices like explaining what the other didn't know at given time. In essence you're retaining your perspective-switching 1st person, except the switches are fully explicit, on another level of the story, which is 3rd person.