What problems arise with gender (he/she, his/her) in English?

Although not a problem in Estonian with "Ta," pronoun reference can be challenging in English. The biggest problem is dealing with an unknown singular person in a smooth way. The student said that he/she was having problems with his/her homework and that he/she did not have time for himself/herself in his/her free time. See? It gets complicated and ugly because we do not have a third-person gender-free pronoun in English.

Here are some ideas:

1. In spoken language,  much to the chagrin of many prescriptive linguists, many people use "they," "their," and "them" when speaking about an unknown gender: The student said that they were having problems with their homework and that they did not have time for themself in their free time. However much it may be used and heard, some will continue to protest that it is just bad grammar to speak this way.

2. A better solution, in my opinion, is just to make the entire sentence plural if possible. Most of the time you can use a larger quantity to indicate the same general meaning: The students siad that they were having problems ... I think this is the cleanest "fix."

3. You can also use "one" but this gets really messy and sounds kind of funny: One student said that one was having problems with one's homework...

4. Another option is just to use one gender (you can write that you did so for stylistic reasons in your foreward, if necessary) and stick to it for generic references. Be ready for some feminist criticism if you always choose "he" as a general noun though. Let's be politically correct!

Which resources did you use to find the solution? Were the resources useful?