3. difficulty going up is guaranteed to drive bitcoin value up
There's no argument I know of that says an increasing difficulty that wasn't itself caused by a higher price would lead to a higher price.
Here is the argument: A higher difficulty makes a 51% attack on the network harder to achieve. Since that is widely recognized, a higher difficulty makes people more confident in the long term viability of bitcoin, which leads to more hording and acceptance, and THAT drives up the price.