Without a concrete example I find it a bit hard to follow your explanation of what the inductive and deductive lines of reasoning would involve. Particularly difficult to understand is this bit: "...wouldn't the next process of subtracting it to a final point be deductive reasoning?"
Still, I think "doing science" almost certainly involves both deductive and inductive reasoning – and beyond these also the practical side of organising and conducting experiments – and sometimes even a more pragmatic goal of trying to achieve a particular goal, to make something that works well for a particular purpose, in other words.
There are these practical problems like your theory and your background knowledge or "auxiliary assumptions" always confronting the world, or evidence, as one unified whole, which means that results don't directly tell you which part is at fault, the hypothesis you're working on or some part of the background knowledge you're operating with. Then there's the problem that inductive processes are always guided by some notion of what the relevant factors are. For instance, when you're testing to see if all metals expand when heated, the surrounding air pressure and the metal involved might be relevant factors, but not, say, the time of day or the colour of the experimenter's socks.
I guess I see "background knowledge" and some kind of evidence or what you call a "base case" as the spring boards for a hypothesis. I see sort of see you as saying that when forming the hypothesis you're reasoning inductively and when refining it, you'd be reasoning deductively or backwards from it. This I don't agree with. I can sort of dimly see what you might have had in mind but am inclined to think that there is much more overlap and interaction between inductive and deductive thinking at each stage than you suggest.
Do you see some problem with the idea that someone researching a problem would use both deductive and inductive reasoning, and even intuitive thinking or guesswork at different stages of the process? I think you typically have a methodology for investigating something, which is to say a method or obtaining what you judge to be good evidence on a phenomenon. Then you have either a sharply defined problem or a dim notion that there might be something interesting going on here, and you set about gathering evidence and trying to make sense of it.
The essential bit really is having a good way of obtaining evidence – something fairly independent of your prejudices and intuitions that you can then grind your speculations on mercilessly :P