This should really be a comment, but it's far to long to be a comment, so meh.
Strictly speaking, the term "gendered nouns" doesn't mean what a lot of people think it means, specifically, sexual gender. All the romance languages that derive from Latin have or had Noun Classes where essentially all nouns fall into one of a number of categories - typically two or three.
The idea, for English speakers who are not familiar, is quite simple. If I want to write/say something like "I brought a chair, a cup, and a sofa from Ikea, but then I dropped it.", you have no idea which of the three "it" is.
Along comes noun classes to the rescue. Lets arbitrarily assign each object a class, say
3 to chair/cup/sofa respectively (as they are in German), and have the pronouns
itz for each class. Now you can say --"but then I dropped ity.", and it's very clear which object was dropped. The cup.
This system helps make language more reliable, however, redundancy always comes at a cost. The cost here being that the more classes you have the more difficult it becomes to remember which class objects belong to. Certainly, it is a case of diminishing returns. Many languages therefore dropped their 3rd class and just stick with 2. Some languages like modern English dropped all 3 and just have 1 (or none, depending on how you look at it). Linguistic experts often attribute this to the invasion of the Vikings into the British Isles, where Old English and Old Norse both had the same number of noun classes, but the classes had different nouns in them, and so the benefits of noun classes were nullified and actually hindered communication, so they slowly lost popularity.
But the number of noun-classes is not at all as important as what nouns you put into what class, and here lies the paradox. If you put nouns that are similar in form or function into the same class, it will be easier to remember which class they all belong to, however, the probability of sentences where multiple nouns all have the same class increases, and the utility of noun class for clarity decreases.
If knife, fork and spoon all had the same class, then classification of these nouns is kind of useless in any given sentence, which is why that is VERY rarely the case in any language that uses noun classes. However, the more divergent or random the assigning of nouns to classes is, the harder it becomes to remember an individual noun's class.
As for 'men' and 'women', well they are also nouns, so they also need a class. Unfortunately, this is where the confusion about 'gender' springs from. The fork, in German, is not female. It is simply in the same class as female. Why would anyone think our ancestors were so illogical as to assign sex to inanimate objects? They just gave their classes the names of the two big classes seen in nature - men, women, and if you need a 3rd class, neither.
None of the above has absolutely anything to do with the OPs problem. The only reason I mention it all is to draw a line under the issue of noun class - something English does not have - with the true issue in the OP; the use of collective nouns for a profession or activity that was almost entirely done by one gender, now being done by the other gender and a new word being coined to highlight the fact that the person described is not of the typical gender, as well as the issue of what to do when gender is ambiguous. This is a phenomena that does still occur in English and is part of an on-going debate in English-speaking communities too. In short, this is not a German-specific issue at all.
The obvious example is Actor. An actor was once a profession only men were allowed to perform. When women started performing, the term Actress was coined to raise awareness that an unusual gender was performing the role. But what if you want to refer to the profession without consideration to the sex of the performer? Is it Actor or Actress? Is assuming one over the other sexist?
Modern society no longer finds this gender distinction to be relevant or fair, and so all gendered collectives are falling out of fashion. Just exactly how this is done depends very much on the activity in question, the people involved, what gender was traditionally the dominant one, etc. And of course, it's a bumpy process. The basic outcomes ordered by how stable they are in society are:
A new term is coined to highlight the unusual gender. Businesswoman. Servicewoman. Actress. Priestess. If the default gender was traditionally female, male versions are unlikely to stick, for example 'murse' for male nurse, 'mid-husband' for male midwife, 'manny' for male nanny, as they are often (unfairly) seen as derogatory.
One of the two collective nouns becomes the default. Actor. Nurse. Model. More stable than segregation method above, but still not that stable, else this entire thread wouldn't exist.
An entirely new construct is used for both genders simultaneously and/or neither gender, but always with no gender having more of a claim to the term than the other. stay-at-home-mum, stay-at-home-dad, stay-at-home-parent, care-giver, etc.
Going back to the OP's question, if you were to go with the Studentinnen und Studenten option then you're basically opting for the level 1 solution. To forcibly use one over the other and insist that you are not using it in a sex-specific way, as was your quite sensible solution, would be to opt for a level 2 solution. To entirely change your personal vocabulary to use words which imply 'gender unknown or no gender' would be level 3, allowing you to use the gendered nouns when needed.... but i'm told by the numerous Germans sitting around me that making up new words is not something people like to do here. Thanks to Shakespeare this is far less the case in English-speaking communities where seemingly anyone can conjure up a new word if it's catchy enough. I suspect in the years to come, and as languages mix more than ever before, there will be a significant rise in 'new words' in German... however unpopular that may seem at first.