Plug into clothes dryer outlet, high V and amperage capability and get a real long power cord with real large conductors.

Yes and then burn up the motor.
Seriously, the amperage rating of any motor tells you nothing about the capabilities of the motor. I love these vacuum commercials that tout 15 amp motor. This means nothing.
 I am sure there are motors that are more efficient than others so they would be capable of doing more work (output power). The output can also be increased mechanically by changing the fan design and so forth. Although, making a vacuum that operates on 220 would allow you to use up to 20 amps(I believe), so the power into the machine can be increased.(a 220 volt motor should be used). Good luck

Of course, new motor (or possibly rewire existing motor) is needed to operate at the higher voltage.

Motor efficiency differences between different motors is only a few to 5%, this won't get you much more oophm, and wont get you any unless the RPM of the driven components changes.

The driven components create the load on the motor, and the ability to do work.

Is this now clear as mud, pun intended.

PS

Huh! Kona P you lost one good adwice from me as I am barred from answering the post for not being an electrical wizard.

First of all, for cleaning carpet the size of the motor is not that relevant.  The most important part is the type of filtering system that you will use.  A bag filtering system is going to restrict your airflow more than a water based system.  The power that you desire will mainly be limited by how much your airflow is restricted on the exhaust side of the system.  Airflow through the system is where you will develope power.

Another point,  if you are developing this vac to produce as a product, then requiring more than 15 amps will not make you competative and will actually hurt you in a competative sense.  Stick to creating a more efficient airflow system and you can get all the power you want.

To get the air flow you still need the power.  The power is used to turn the impeller (the most important part) of the compressor generating the flow.  Minor losses by things such as filters can be overcome by increasing the filter size or like motorz said, change the filter medium, or maybe use a 55 gallon drum on something like a hoover, now that would work.  Its pretty standard, people have been making vacuums for years.

And movement of CFM's requires power.  The more you move the more power it takes, that's a standard science too, again, people have been moving air for years.  You could try to invent a 100% efficient electrical motor, now that would beat the competation, and think of all the money you would make putting a motor like that into vacuums!!!!

Or you could decrease the density of the air, maybe by strapping an York heat pump on the front of the vacuum and injecting hot air into the carpet.  I have not seen that on TV yet.

I think PacificSteve has the best solution so far!!!

But what do I know, I am not an electrical engineer...