Do they need to meet (often)? No. I think the story works well enough without forcing them together. Although, as Amy observed years ago, it was pretty much two stories most of the way. In an earlier draft on which she commented, they had no interactions in acts 1 and 3, and virtually none in act 4. That was three quarters of the book. I think the Royals Forum fixed act 1 well enough. I don't know if there's much more I can do to bring them together (electronically or otherwise) in acts 3 & 4.
Although, after Joseph and Paul escape slavery and go to the palace in search of Apollo's assistance, instead of them being shot, I could have Joseph and Apollo meet again, but I then still need Joseph and Paul (or Joseph and Catherine) to end up in "Heaven", the nickname for the prison where Joseph and company end up, so named because of it's high mortality rate.
I can't see Apollo being angry enough at Joseph to throw them into that prison, so it would have to happen after a face to face meeting. I suppose they could leave the palace, perhaps with special Imperial identification to get them all the way back to New Bethlehem. Something goes wrong, and their IDs are lost or stolen.
Of course, all this is in addition to everything else that has to happen during the chapter in which Apollo and Joseph meet, which is fine since I have plenty of room to expand my chapters in novella form.
Not much opportunity for prolonged tension between them, though.