Hi I doubt you'd be induced for what sounds like fairly standard late preg issues. Maybe MW can offer a sweep to get things going instead.
Get yourself some Zantac for the heartburn. I took it without presecription at the end of my first pregnancy - only thing that kept me sane as the HB was hideous, hideous, hideous. Been presribed this time so that helps enormously and has really improved being pregnant!
I also have mobility limiting SPD so i know your pain very well.
Sorry to hear you're feeling uncomfortable and miserable - I'm 39+3 and feeling very much the same, I sympathise!
I think given that you're experiencing what pretty much all heavily pregnant women are, it's unlikely they'll induce you, but do discuss it with your MW when you see her because there may be things they can do to make you more comfortable for the time being.