I don't think you need to war right now, most of your improved cities are cottaged so their production isn't that great.
Conqs against a pre-Gunpowder Civ is one of the biggest STRENGTH_OF_TECH_LEAD_MILITARILY / EFFORT_NEEDED_FOR_SAID_TECH_LEAD ratios in the whole game, certainly better than almost any rushbuy based attack I can fathom. I wouldn't pass on the opportunity especially since it's just ~15 cities after which victory is guaranteed. A couple of prod cities + the whip (which can be used liberally) is very much enough prod. Afterwards tech will skyrocket in 50 turns so for now the only tech worry is to get into the winning position - already gained with this setup. For a related game story, in the recent IU-Justinian I basically limped to Steel, had 86 bpt at ~1500 and subsequently 1100 bpt at ~1700 after the winning position was gained. Science doesn't have an absolute value

That's not to say emphasizing economy here would lead to bad results, I just think it will almost definitely result in a more tedious and harder victory.
The question in my mind is whether to aim for economic techs like Democracy/Communism after Conqs or ensure your military triumph by going Steel and/or Rifling next. Both have their pros/cons.

