Trying to provide a positive role for the teacher, if you only see your students in Years 10 and 11, I would regard improvement in spelling as a low priority. Depending on the individual, there might be marginal gains in focusing on the high frequency words that they spell wrongly with a target of one or two words/week. If you can discover how they actually learn spellings (they must do so, unless every word is wrong!) then removing something like 50 – 100 common errors is quite an achievement. An alternative target is important specialist words in subjects where they have to write these words. There would certainly be value in getting technical terms in history, geography or English literature spelt correctly.
For the wider picture, just train them to use a spell checker, like the rest of us! Making it clear this is how they should operate may be liberating for them.