Bear in mind that by moving the woofer around you are altering the position of the bass driver. This is similar to moving a speaker or raising it on a stand. If your subwoofer is 2 feet high then if you turn it upside down you have rasied the woofer by two feet.
Two feet corresponds to a quarter wave cancellation of around 130 Hz ( a suckout ) - since most subs have plenty of output at 130 Hz then you will get the smoothest response by keeping it downfiring. If you tuck it up against a wall then you'll get the smoothest response.
Of course room modes will be more severe with a wall or corner placement - so "in theory" you can try to play around with position to get the most even response at the listening position by balancing quarter wave cancellation with room modes. In practice this is very hard to do as they hardly ever line up so that they cancel eachother over the sub bandwidth and you lose dynamic range in doing so (the sub is most powerful placed up against a side wall or corner). Generally a corner placement with down firing sub will give you the most dynamic range and smoothest response but this comes at the expense of overly strong room modes. Often a side wall placement with downfiring and pulled out from the wall where you have the speakers seems to be a suitable compromise - in this case the quarter wave cancellations from floor and side wall are eliminated and the cancellation from the wall behind the main speaker is not severe or deep because of the odd geometry between you and the sub.
Two feet corresponds to a quarter wave cancellation of around 130 Hz ( a suckout ) - since most subs have plenty of output at 130 Hz then you will get the smoothest response by keeping it downfiring. If you tuck it up against a wall then you'll get the smoothest response.
Of course room modes will be more severe with a wall or corner placement - so "in theory" you can try to play around with position to get the most even response at the listening position by balancing quarter wave cancellation with room modes. In practice this is very hard to do as they hardly ever line up so that they cancel eachother over the sub bandwidth and you lose dynamic range in doing so (the sub is most powerful placed up against a side wall or corner). Generally a corner placement with down firing sub will give you the most dynamic range and smoothest response but this comes at the expense of overly strong room modes. Often a side wall placement with downfiring and pulled out from the wall where you have the speakers seems to be a suitable compromise - in this case the quarter wave cancellations from floor and side wall are eliminated and the cancellation from the wall behind the main speaker is not severe or deep because of the odd geometry between you and the sub.