The South direction covers more than just due South. Other than doing a little construction regarding the door direction, one can shift the door witha hexagram in certian situations, but not much. With what you've said about the degree of your front door, a hexagram would be able to shift it enough.
Another option is checking with a coach her at Learning Strategies regarding setting up a hexagram that will at least lock the front door direction on the best possible energy of within a range of degrees of the front door.
What that means, is that even though we won't be able to shift your door off the South direction with a hexagram in this case, the degree your door is on, and each of those degrees to the left and right "color" the energy coming in the door with a different intention. Marie gets into this in her Advanced Feng Shui trainings. So even thought South still stays your total loss direction, there may be a degree within a certain range of your front door's direction that can be shifted to, to at least give the energy a better influence as it comes in. A hexagram for that degree would be made and placed above the door to lock the door to that degree/energy.
It may not make sense to you, so call in and ask for a Feng Shui Coach at Learning Strategies and they'll help explain it.
As for the tiger...
You can look at putting something tall to the left of you as you stand at your front door. A plant, bush, statue, crafty thing, etc. so you have that height support right away as you step out.
Much Love, Shawn