First, it's good to have actual scientists (in training) asking questions on SE.Philosophy!
Does falsificationism apply to scientific practice?
You seem to be bothered by the observation that the scientific practice in your field doesn't conform to Popperian ideals of falsification(ism).
Well, the good news is that no scientific practice conforms to Popper's ideals, so you're not alone.
Indeed, Popper's theory has no pretence to describe scientific practice, it is a normative theory, its aim (at least starting with Logic of scientific discovery of 1934) is to postulate ideal methodological rules.
are there synonyms or alternative terms for this [i.e. my] type of science?
Yes, real science! :)
And there's nothing particularly metaphysical about that. The notion of "metaphysical research program" is not directly relevant to the problem you articulate in your question. (Feel free to ask another question if you want to know more about it.)
Falsificationism and the problem of competing hypotheses
Going into the specifics of your question, you write that in your field it is
potentially impossible to conduct realistic experiments that achieve the ideals of Popperian falsification
but the specific point you are concerned with is that
alternative hypotheses are difficult to falsify. Papers on the topic (including mine) are fraught with phrases with like "the data are consistent with the hypothesis of allelopathy" but neglect to mention that the data are not necessarily inconsistent with alternative hypotheses (eg, competition).
Your problem is difficult to address in the Popperian framework because falsificationism addresses theories, i.e. a conjunction of multiple hypotheses (plus other things), not a single hypothesis.
Popper was aware that data may be consistent with multiple competing hypotheses and that is why he thought that sophisticated falsification happens at the level of theories, not hypotheses.
While two competing theories may overlap in many of their predictions, they might not overlap in all. So there's at least one pair of competing hypotheses that predict two contrary experimental outcomes and that can be used to stage a crucial experiment. This experiment can rule out one hypothesis, thus falsifying one theory, while the other theory survives.
(Please note that the logical possibility or factual existence of crucial experiments has been disputed and debated for a long time. Popper's own theory was a response to Pierre Duhem's view that crucial experiments are a logical impossibility. This is called "contrastive underdetermination". See the problem of underdetermination of scientific theory by evidence for a background discussion.)
Even according to Popper, crucial experiments are rare. It is normal for scientists to work with data that is consistent with multiple hypotheses most of the time.
Curiously enough, there are also enough scientific problems for which scientists have struggled to find any viable theory and are happy when they find one. No wonder that they disregard the philosophical discussion about competing alternatives to be highly artificial. I wonder if this is specific to certain sciences.