I had SPD (needed a wheelchair to cope with Bluewater by 7 months, left work early), and an easy, easy labour. The pain-free distance is very important though - if you get shoved around it could cause damage you can't feel at the time, but will come back to bite you later. I had a obs. at the hospital do an internal at 8 months that left me hardly unable to walk afterwards, but my midwives for the labour itself were really clued in, and very careful not to cause any harm. I didn't need any internal exams (they could see from my breathing and temp. and the baby's heartrate that all was well), gave birth in water with just gas and air, and the pain from contractions honestly wasn't ever that bad. I am a wimp, too. Need to take pain meds to get my legs waxed, am scared of the dentist, you name it, I try to avoid it. I had nightmares before having ds about how painful it would be, totally freaked out on the subject. But it isn't that bad for a surprising number of women - there's a thread here on that, actually.
Unfortunately my SPD is still very faintly reminding me to be careful if I overdo it now, almost 8 months post-birth, but it's an echo of what it was. I'm double jointed and began to suffer at 13 weeks, so really not a great candidate for a fast bounce back. You may be luckier. I'm also feeding my son, so the hormones from that may still be having some effect.
I'd definitely fight for the pool all the way if possible as it supports the ligaments and joints. I actually felt less pain than I had in a long time, contractions or not, when I first went into that pool. It was bliss. My SPD at its peak was a shedload worse than my labour - and you get drugs if you need them for the latter, too! And whatever you do, avoid stairs in favour of lifts; if you can't, take them one at a time.
SPD and morning sickness were horrible - labour was a comparative cinch. I'll have far more fear about the horrors of being pregnant than giving birth next time; your GP can't ever have had SPD! And I was told by my physio that some women with SPD are believed to have easier labours because their pelvis is so open! That's what the ligaments soften for, after all.
I would get it written in your notes, in capitals, that you have SPD, and the safe separation distance. And then I'd make sure your birthing partner is willing to fight for you tooth and nail on the point, because if you're anything like I was, you'll be so stoned on the gas and air the midwives will be talking Greek and you won't be able to string a sentence together.