I'm guessing the delay in Archery meant a lack of units fogbusting and you had some problems with Barbs. With a gem start and all those forest 1600 BC and 7turns from Math seems somewhat behind pace. I know you said you forgot to reasearch it sooner?? If so go back to previous save cause this is a HUGE hammer delay at this point in the game. In my game I actually stole a worker from Ragnar which definitely sped things up for me (and slowed him down). I had Math at 1880 BC and had settled my 5th new city by 1240 BC.
Tip - stealing workers from AGG AI's is almost always a safe bet because they will make peace quick. Ironically peaceful and regular AI's (especially on Deity) take forever or don't give peace. It's why virtually every top peaceful Hall of Fame game uses Agressive AI's as a game option. It makes stealing workers (even on Deity) viable, slows down the tech pace (makes the units you have last longer!) and lets you bribe, declare, peace almost at will.
Your game. Where to go from here? I'd say settle 1 or 2 more cities while teching towards Construction and make an attempt with an Axe/Spear/Cata war vs Ragnar. Try to bribe in Cathy to war as well otherwise she'll focus on you. I made the comment in my previous post that even if you had lots of land to settle the quality of your neighbors would make it impossible to do. Imo you're forced into war sooner than later. While it would be nice to settle more than 4 or 5 total cities, given your current situation, you really don't have time.
Good luck and keep us informed.
edit: Why aren't you using Bat (bug and bull combined) or some other useful tool/mod. It makes whip overflow, AI plotting, power rating, what they will trade, when they will take peace or capitulate, overlays, map finder tools ^, etc etc. Really, I couldn't play the game w/out it.