I'm not entirely sure on the woodworking front. Higher-level synths in things like goldsmithing and smithing are where most of the money is at, but I reckon shihei are still a reasonably profitable synth for mid-level woodworking. Particularly so if you also have mid-level alchemy to make your own black ink.
The farming part I don't really know about lol. Most of the higher-end gear these days isn't purchased with gil anyway; bayld, plasm, cruor, etc. Higher level THF/DNC could probably farm sky pops fairly easily, and then if you got a friend or two together you could pop the gods and sell seals and tatters, though the market there is a little soft lately because of the login campaign. You can also do Dynamis solo on THF/DNC with a reasonable level of profit for your time, even with currency prices being on the low side until SE decides how they want to handle relic weapons post-SoA.
COR not exactly the best farming job, I guess is what I'm saying. XD