I had savage SPD (in every joint in my body, not just my pelvis!) when pg with DD2, I had a lovely, easy, painless homebirth, and my joint pain was never even discussed as a reason to go into hospital.
Get a birthing/gym ball and sit on it, it will help to strengthen your core muscles and really helped my back pain. I leaned on it (knees on the floor, chest and arms and chin on the ball) to give birth, didn't have to spread my legs wide like a hospital-on-your-back-in-stirrups birth so the SPD was never an issue with my labour or birth.
I had hideous SPD and I had a lovely homebirth. It was very quick and easy.
SPD is caused by an excessive amount of the hormone relaxin. It makes your joints so relaxed that the baby passes through your pelvis easily. The reason you have so much pain with SPD is that the relaxin makes your joints so lax that you find it a nightmare to walk.
Homebirths are great for SPD because there is no temptation to ask for an epidural.