If you mod anything, your chances of reproducing the same world is slim. Vanilla 34.11 currently produces the same identical worlds if you use the same seed, from one install to another, even cross platform.
If you change any raws though, you're on your own.
A few things to comment on regarding your list of desirable traits. Some of these traits are opposed, so you'll have some difficulty.
Making thin worlds (those with few z-levels) is possible, but you need at least one cavern if default dwarves are going to survive. You can make a world as little as ~20 Z levels between embark and the circus, though, if you take out caverns and give dwarves surface farming.
Generally, I don't do anything special to get clay and sand.
What civs you get depends on what biomes you provide. If you provide all civ biomes, you get all civs. This is true for humans, elves, dwarves, and kobolds. Goblins will live almost anywhere (except Good biomes). Getting a large number of distinct biomes (different names on the map) will allow for a large number of titans and forgotten beasts, as only one is generated per uniquely named area. One per surface region for titans, one per belowground region for forgotten beasts.
Getting unique biome names is easiest with varying elevation. This of course makes it more difficult to find flat embarks.
Ramping up volcanism makes it easier to have volcanos and magma, but harder to find iron or other sedimentary stone/ore because volcanos are igneous.
Some of these problems can be avoided by lowering mineral scarcity to under 1000, but in some cases it's not enough to get the volume of resources you want, if you only have a few z-levels to work with.
In these cases, personally, I use dfhack to adjust my embark area, after I pick it. If i need iron ore, I'll add it. If there's no water, I'll add it. If there's no magma handy, I'll add it.
You can spend hours (or even days) generating worlds to try and find one that is just right, when a few commands in dfhack, on any map, will give you magma, fresh water, and all the ore/stone you want. I'm not saying it's the only way or the right way, but it does save an enormous amount of time. In particular, as is your case, Thuellai, when your goals conflict with the way worldgen "normally" works.