I'd love to hear more about no-teching; how do you make that work?
Also, my specific problem with the jump from Regent to Monarch is that I'm just way behind the AI. Is the solution to just run scientists, cottage the rivers? I'm used to being behind the AI early on from the newest two Civ games, but for Civ 4 I never really played any higher than Noble-Prince.
For no teching it'll only work for some civs, obviously. With Canada, the goals just require you to create culture, horde gold (to end wars), and pump out a lot of settlers and workers. Given that, there's no need to research techs (just stay on America's good side). For Indonesia, the goals only require you to have a large population and some happiness resources. No need to conquer, no need for any wonders, no need to reach any tech milestones. The Spanish will invade the Philippines, but stacking archers and catapults can wipe out their tiny stack. You'll later have to deal with the Dutch attacking three of your cities, so I researched Machinery, to upgrade to crossbows (the Dutch will have more advanced units than the Spanish did). Other than that and chain irrigation, there was little reason to tech. Actually, in that example, it's also better to avoid techs, because then you can avoid stability checks (let's you grow cities in Australia without your empire collapsing). There are probably others where the goals would see the commerce better directed towards culture or wealth, but those are the two I've done so far (quickly looking at it, Argentina looks like one where it might be unnecessary to tech).
Noble difficulty is where, I think, everything is on par with the AI. Higher difficulties will require you to trade and use other tactics to ever get a tech lead, since you tech so much slower. The scientists are useful because they normally produce 3 beakers. This would be the equivalent of a village (prior to printing, not on a river) with science at 100%. Since goals for certain technologies are relatively short in time frame, it wouldn't make sense to invest in a cottage when you could run a specialist. A river tile is a bit more sensible to run, since a hamlet will be the equivalent to a scientist. However, main benefit of specialists would be great scientists. Bulbing techs can you place ahead in science (long term, an academy would probably yield more beakers, but it's usually not a good investment in this mod) and this is where the key is. As long as you have techs which others don't, you can work out deals. This is one of the nice things about being in Europe, you have a bunch of civs to trade techs with. So, for instance, as England I can get great scientists out really quickly, so I can bulb a lot of techs along a specific line and then fill in the gaps by trading with Poland, Russia, Italy, and Portugal (which will compensate for France, Germany, and even Spain's tech rate). If you fall too far behind though, you'll never have any leverage over anyone. For example, if you're in Asia for a 3000 BC start, you'll never get any tech before China does (Korea and probably Japan are both impossible on a 3000 BC start on Paragon, unless everything goes to horsehocky in the simming). Even on 600 AD, Mongolia needs to be the great equalizer, since they should force China into collapse or at least capitulation (similar to real life, actually). Now, a lot of areas on this map have a lot of food (you'll never have this many good city spots on a normal game of Civ IV), so you'll probably have no issue running both cottages and scientists (in England, I cottaged every river tile for Norwich [NE of London] and Chester, while running 2-3 scientists). You'll just need to manage each cities' tiles to work with what would produce the greatest research output.
I will admit though, I've only recently begun playing this mod and a lot of civs I haven't tried yet. Japan and France in particular look extremely hard, since you need to stay in a technologically strong position (France for wonders, Japan to be a leader in the Global and Digital eras), produce an exorbitantly high amount of culture, and perform a lot of conquering. Anything which requires a combination of gold, science, and culture is infuriatingly difficult, since they share a commerce slider and it forces you to build more buildings than you normally would (culture buildings especially are almost always useless normally).