Muslims claim they do not treat Muhammad as a partner to Allah, but I've never been able to reconcile that claim with their actual doctrine or practice.

How would we know? May be you have been hanging out with not too knowledgeable Muslims in your country I am afraid...you need to discount the devolution some of those might have gone through in the days of their bondage of the colonialism in their lives...

but still you need to describe what have you observed so it could be clarified ...

  Clearly, Muhammad occupies a central place in Islam, unlike any other human, but in many ways similar to Allah.  To be sure, Muslims will acknowledge that Muhammad is subordinate to Allah, but the sin of shirk does not stipulate equal partnership, and it seems to me that a junior partner is still a partner. 

Central as Human being of course not divine. just the slave; How  does slave gets to be junior partner?

You are  trying to be prosecutor , judge and jury all at the same time!

You have failed to present any evidence and have reached to your indictment , you are not a juvenile to act that way?

There are sixty four signs in Quran (http://www.islamicity.com/QuranSearch/ ) just add partner in the search/ that clearly preclude this assumption of yours! ...As a matter fact this flies in the face of Allah's rejection of  Christianity's main argument of trinitarian partnership theme

If you study the daily salaat x5  that has a supplication at the end that gives privileged position to Prophet Abraham after declaring there is no partnership to Allah and Mhmd being Allah's slave and a messenger...

Consider the following: Muhammad is treated with a degree of reverence that for all intents and purposes is indistinguishable from that for Allah Himself.

People in his time recognized God due to Mhmd's character, efforts and struggles unmatched in the annals of prophetic efforts and accepted the words he got. What they saw must be a lovable soul and they did give him what he deserved the love and reverence,

He was the only messenger who had completed the task at hand... still was concerned and worried as protector for his nation till eternity like a father more loving than real fathers when it came to save and redeem.

  To insult the Prophet is to commit blasphemy.

Not a new standard as regards to Allah and his prophets...The people who insult the prophets are the party of Satan and regard this as blasphemy is self explanatory; any one dissing your beloved will invite the condemnation ...It same about everything else in this world...What is so strange?

  Muslim prayers, though not directly addressed to the Prophet, mention him frequently.

Well that was what he was told to practice by the boss(Allah) And he let the believers in on the preferred and accepted process! Consider this like a investment policy, say peace(salaam) one time and u find peace ten folds... which believer would not like to have this bargain?

He is considered infallible in matters of doctrine.

In fact, his statements and his actions are doctrine: the hadith and sunna sit on your bookshelf alongside the Quran, and are considered similarly authoritative.

According to the Prophet the Hadith were not to be recorded while Quran was being revealed to keep Quranic authority perspective clearly supreme...That should tell you something ...

What kind of argument is that Hadith and  Quran are next to each other on Muslim household shelf?

It is absolutely a laughable argument... They are separate books and class ... I have bible and book of Mormon and few others texts sitting on the same shelf what difference does that make?

Would you have liked if  Muslim had done the same as the Christian did to theirs, mix up Jesus's hadith and sunna with what God had revealed to him? Then he did not establish anything before his going away...

So my question is this: how would your beliefs or your behaviour be different if Muhammad actually were a partner to Allah? 

It is a very sly proposition cuz you are going into a hypothesis that would be similar world that was created by merging Christian dogma with Roman's mythological religion!

It would be a sepia version of Christians or Muhammadans (if the 64 signs had been taken out of the Quranic narratives I can't think how) as the westerner colonist used to label the vanquished Muslims...To get there you will need to revise the world history also...That is a tall order..There would be no Muslim and Islamicity to read this!

By now there will be a new concoction a cross between +tains and so called Mhmdns or may be not if the so called Muhammadans had been on their war path without mercy probably there would be no Christians left in the 7th/ 8th century Mhmdn empire...Any more of your hypothesis...

Who the heck would worry about shirk? the concept would be out of the lexicon...