For consideration for solving this problem and the problem posed by http://phylomon.forumotion.net/phylomon-f1/playtest-report-scoring-system-unbalanced-invasives-too-good-t68.htm
regarding invasives is to tie it into the points system.
I have noticed the first thing my daughter does is look at the point value of the cards.
An undesirable species like a rat or an invasive should have very low points, or possible even zero points, so the benefit of playing it is not to boost yourself but to impact your opponent.
Even then, there should be a consequence because it's not a desirable action, so that consequence might be to lose 5 points from your total score. So then the challenge is to decide whether the consequence is worth the benefit of impacting your opponent.
To take it a step further, as mentioned in another post, some event cards could be a compulsory play as soon as you pick them up. In that situation it then becomes important decision making as to how you play the card. e.g. if you pick up Drought, and you have to play it, and consider a requirement that you have to play it on yourself, then you will likely try to play so that it has the least impact on yourself which is a desireable, overall, learning outcome.
Let's consider that it is not madatory that you play it on yourself and that you have a choice, but a condition may be that if you play it on your opponent you ADDITIONALLY suffer a 5 point loss that you wouldn't get if you played it on yourself.
Using point scoring as a control mechanism could solve some of the problems about cards being considered too strong or too weak.