The problem is I'd like to manually increase the yield of a particular tile. Since there's no SetYield, my thought was to intercept GetYield...
Nice idea, and that's something I wish they'd put in the game from the start. I've wanted to have my advanced Terraformer unit be able to just boost a tile's yield by standing on it each turn, in addition to the worker actions, but I haven't been able to get that to work because of the lack of a good SetYield function.
But if you can't get the full Lua hack to work, you might be able to get the effect you want in another way. For instance, you could add a custom Feature with no graphics that adds the yields you want, and simply place that yield on the tile you want modified through the appropriate events. (This'd have problems stacking with forests/jungles, and you wouldn't have a lot of flexibility in the yields in question unless you added a whole set of these.) If this is supposed to be a temporary effect, then just remove the feature at the right time.
I did something similar in my own mod; I wanted my new Empath specialist's great person to place a new Monolith terrain improvement (analogous to the Academy/Manufactory/etc.) that added Happiness. So all I did was trap the OnImprovementCreated event, check to see if the placed improvement was IMPROVEMENT_MONOLITH (+2 food, so that the AI will see the tile as valuable and not try to replace it with some other improvement), and if so, place FEATURE_MONOLITH on the same tile with the happiness benefits I wanted (since Features include natural wonders, and so have a happiness option) and -2 food (to cancel out the improvement). It's not pretty, but it seems to work well. If you don't want to play around with Features, you can also do this through tweaking other tables, like Plot type, although that's usually tied to a slew of graphical effects. So, you end up getting the yield boost you want, without having to actually edit the tile's base yield.
I can think of two other ways to do this (unbuildable, repeatable buildings, or a flat Lua yield hack), but both of those would require altering all of the yield UI routines.