No, "more workers" are still not enough! Build at least twice as many...
Ok, seriously: "more workers" is indeed one of the few strategies that are easy to adopt and which apply to "both worlds", the player who likes to play just for fun and plays his own modded variants like timerover51, and the player who likes to compete with others and compare his results in the un-modded game with the legends of the past.
For the latter kind it is important to note that we should talk only about the "un-modded" game. Even though I consider myself a player of both worlds (once in a while I like to play a scenario or mod for a completely different game experience and to avoid boredom, but I also enjoy the competition and discussions in the GOTM community), I have to say that it is not a good idea to mix arguments concerning "modded varaints" with ones concerning the "un-modded base game". This would be comparing apples with oranges. For example, timerover51, in a game where you mod the Pallace or Pentagon to auto-produce leaders/armies a military victory will become much much easier than in an un-modded game. And also the tips in SirPleb's war academy article about "leader farming" may not be so important to you as they are to us when we play the un-modded game.
So my first rule for strategy discussions would be: only discuss the un-modded game (unless the thread explicitly states that it is about this or that variant, which would then have to be one that can be publicly downloaded from the Modder's Forum, not one that exists only on one single player's hard-drive.)
Having said the above, I want to challenge your statement "Mine style does not follow the War Academy". Of course the articles in the War Academy are of variable quality and some may indeed be a matter of style (for example I never build any artillery units - at least not in single-player games of difficulty lower than Deity - even when playing for the GOTM competition - so in that point I "don't follow the War Academy" either...), but I would say that many of the War Academy's articles discuss topics of such general or fundamental relevance, that they could be beneficial to both: the un-modded game as well as your variants.
For example:
- A worker works pretty much the same in every flavor of Civ3 and tile improvements are always important, adding shields, food or gold to your economy. (Unless you are playing a mod which starts already with a fully improved and settled map.) So detailed analysis of early worker management will benefit your playing skills as much as a GOTM of HoF player's skills.
- The corruption model is pretty much hard-coded in the exe, so will be the same in any type of Civ3 game. You can tweak the properties of each government a bit or play with different corruption-reducing buildings like courthouse or police station, but the underlying mechanism remains the same, so a deep knowledge of that will again benefit everyone.
- The underlying basics of warfare should be another example. You can add different types of units to the game, but a good grasp of the general strategies and tactics of Civ3-warfare, will give you an edge in any type of game that contains warfare.
- I think it is not possible to add new civ traits to the game. So even in a variant game the tribe you lead will have some (possibly more than the standard 2, possibly less) of the 8 existing traits. You will benefit a lot, if you have well-founded knowledge about how to best leverage the power of an agricultural civ or how to make the most out of the expansionsit trait, etc.
There may be more, but this is just to incourage you to give the War Academy (or the Training Day Games, the legendary Succession Games or the GOTM discussions) a "second chance". There is a lot of wisdom in these resources, and I'm sure you can still learn a lot about our beloved game, even if you do not "care for the HoF" (which I don't do either, by the way...

).
In any case, in order to answer Glububble's original questions: yes, if you want to understand how the old masters achieved these incredible results, there is no other alternative than to study the intrinsics of the mechanisms they applied. And these mechanics are most prominently documented in the War Academy.
Of course it is tedious and takes a lot of time. You will have to read a lot, some stuff will be a revelation to you, some stuff will lead you on a false trail (because it is outdated, e.g. was written at a time when only Civ3 Vanilla was available and then later changed in one of the subsequent patches/versions and nobody cared to correct that strategy article since then...

), but slowly but surely you will advance on the road towards mastery. However, it won't be easy, it's like chess: someone who just learned the moves, can probably not reasonably expect to become a Grandmaster in the course of a few weeks... Prepare yourself for a few years of intense study and research.
Cheers, Lanzelot