Could a person do the shinigami deal without losing half his lifespan?
There are a few things wrong with your theory:


Death by Death Note doesn't count in the user's lifespan. Even if you have 80 more years to live, if I write your name down now you die 30 seconds later.
A Death Note will not work on someone with 12 minutes or less left to live. According to How to Use: XXIX.


So no, the user would lose half of his original lifespan. The only way to extend a lifespan is to get a Shinigami to die for you.