As expected, it's really about not letting people have pleasure

[Rev Dark]

Sorry BA, it is neither reasonable, nor rational; the effort is there, but it is deeply, fatally flawed on multiple levels.
Process of Democracy - specifically in law is that the law is applied equally to everyone.  So your proposal can be interpreted two ways.

• The first is that the blastocyst.fetus is a person.  This fails in that, based on you plan, not all all treated equally.  Some are protected (following the third strike) while others are not.  This breaks Process of Democracy.  It also does not answer any questions as to the rights of any fetus being carried to term by an individual.  I will address this point further later as it is very important.
• The second is that you are punishing women for their reproductive choices.  This is just misogynistic;  I know you mention the role of men later, a point I will be coming back to. 
  
• Neither of these points addresses 'morning after pills' and similar after fertilization contraception.  Are these mechanisms Class A strikes, Class B strikes, foul balls or another baseball analogy?
  

Strikes WILL count against teens that have consensual sex. Even if they
used contraceptives - if they're using them then they should know the
risks.

So you are treating teens like kids in regards to voting, drinking, and crime, but take special exception for their reproductive behavior?  That is just creepy.  You are also making the rather egregious assumption that they are informed and know the risks.  There is a woefully large percentage of the American youth population that has been let down by their educators in regards to sex ed.  Why not go with contraceptive implants that are removed when the individual reaches age of authority?

Also, the male parent gets a Strike as well, whether or not he's in support of the abortion.

Which requires forcing a paternity test on all abortions.

Why so stringent? Because if he's sleeping with a woman then he knows
the risks as well. He needs to be held responsible for that - even if
the woman gets the abortion against his wishes (she could just give the
child over to him to care for and leave him if she doesn't want to take
care of the child).

This breaks down in practice.  You are holding an individual responsible for things that they have no control over.  If you are punishing the male parent, they should have choice in the matter; being able to force the pregnancy to term - which is again, creepy in the extreme.  I will assume that your class B strikes also apply to the father?Practical considerations - National Abortion Database?  Monitored at the state or federal level?

To further clear up moral ambiguity, Strikes can be divided into two
classes. A 'Class A' Strike is the nastier sort. This is given to
mothers who are healthy, are pregnant through consensual sex, the fetus
is biologically viable, and they have the means to care for the child.
In other words, they have no excuse save that it would be
'inconvenient'. Three of these and you face prosecution.

So how do you judge means?  Again this goes against Process of Democracy.  Income?  Number of extant children?  Marital Status?  Psychological Profile?  Employment?  Education?  Any or all of the above?  Whatever mechanism you use, you will have to be able to apply it consistently for every case.  I should also note that every single abortion would have to be subject to judicial review; as your three strikes law would necessarily have to have some sort of sanction for those reaching the third strike - chemical of physical sterilization, imprisonment, etc.  Oh and all miscarriages and stillbirths will also have to subject to examination and review to ensure that they were not deliberate attempts by one or more parties to be artificially induced.

Your proposal also does not really address whether or not the blastocyst/fetus/baby is a person under the law; or at what point they become a person under the law.  From your description it is black or white.  Abortion is abortion if carried out three days after using plan B or at nine months.  Personhood under the law is hugely important in this debate is hugely important because of the implications to the mother.  For example, if a fetus is a person under law, then any behavior by the mother, such as drinking, recreational drug use, or even medical treatment for existing or developing condition - anything that put the fetus at risk could be subject to legal sanctions.  Children are removed from abusive households - how would such things be handled similarly for equivalent actions during pregnancy.  Is the woman taken into custody for the duration?

Abortion is a difficult topic; there is no right answer, or best answer, all we can hope for is the least worst answer.

Shayne