Try a High to Low game with your usual settings. I suggest to NOT use BarbCivs, Final Five, Start as Minors when using HighLow.
Your first civ you can play as your usual, but possibly from the 2nd civ and definitely on the 3rd civ, being on the bottom of the scoreboard, you'll definitely have to do some fighting as most if not all of the territory will be already settled, and not by your previously incompetent (or just really unfortunate) current civ.
Personally I start on Noble and some map that allows for separation of civs until late game.
Totestra (my personal favourite) on the larger sizes gives you continents with very natural-looking terrain separated by massive oceans.
Starting on Noble allows to get through the early eras quicker, later on I either manually set a higher difficulty for myself, or let Flexible Difficulty do its job. I find the most interesting stuff happens from the Medieval era onwards: more unit variety, established empires, ocean exploration, in general more choice of what to do and how to do it.
Or experiment with something completely unusual!
Boreal with Terrain Damage and Movement Limits ON makes it a challenge just to explore your surroundings, the Nomad leader trait suddenly is powerful, and the Arctic Combat promotion fundamental.
Ring maps (iirc the right name) give you a very long and narrow map, a-la Ringworld. Expect to have uncontacted civs well into the Reneissance, and the whole map probably won't be explored until late game. If playing with Revolutions, distance instability will become a major factor once you expand beyond your starting continent.
Add some house rules!
Research by columns: all techs in a column must be researched before going to the next one (no beelining!)
Upgrade only GG-led units. Suddenly choosing whether to settle that GG or attach him to a unit becomes difficult. And have you ever thought about GG-led siege units? The Charismatic leader trait is ideal for this, less xp needed for each promotion, especially as you'll have to constantly crank out new units to replace your suddenly obsolete army.
Dare to mod the xml files?
Archer bombard: despite the name, I find it makes more sense only on Siege units (Civ represents strategic ranges, not tactical). Edit the unitinfos.xml file, remove the Archer bombard ability (set the range to 0) from all archery units, and discover how artillery is supposed to work, instead of single-use city kamikazes. Wish I could make them gain exp for each successful ranged attack, but I guess that's python magic, way beyond me.
Extended High to Low: increase the number of civ changes. With 5 you'll probably already arrive to the late game, put in 10 and the game will probably get to the Transhuman era before you can switch through them all.