I don't have a lot of time, but want you to know that I sympathize. An induction can still be an awesome birth experience!!
I was induced for my first baby--non-emergent and probably unnecessary. My midwife "stripped" my cervix and placed a half of whatever pill they use to ripen the cervix up in there. That was at about 8 am.
The mw "allowed" me to go home and wait for labor. By noon-ish, I was having my first contractions. This being my first birth experience, I didn't know what to expect, and kept waiting for it to get as horrible as everyone told me it would be before going to the hospital.
So I stayed home and labored intuitively, staying active with housework and upright/hands and knees/squatting the whole time. Oh, I did have a *little* nap btwn the induction and when the first ctx started---I highly recommend it! I also ate a lot---vanilla milkshake and fries, haha! Earlier that morning, lots of water and fruit---I guess I was a little scared of pooping

and wanted to be "empty" so I waited to eat a big meal til right before the birth. Took a shot of castor oil for the same reason--wanted to eliminate anything in my bowls and be sure the induction "took". Anyways . . .
I stayed home way longer than I "should" have, and I'm really glad, looking back on it. I was moaning and crawling around on my floor. About 5:30-ish I was thinking "this is really it" and had to moan through the ctx. Still was waiting for it to get as "bad" as it was "supposed" to, and it never did, even though I was experiencing induction ctx which are supposedly so much stronger than natural ones.
I estimate that I got in the car around 5:45? I couldn't sit or buckle, was basically turned around backwards and bearing down against the back of the seat, squatting on my knees. I was bearing down this whole time and didn't even know it. I just was listening to my body, staying calm, breathing, staying as upright as possible, and making noise as it felt right.
I got to the hossy and the nurses were the worst part of the whole experience. My mw had been called before we left the house, but it was going so fast . . . I had to stop and bear against the wall several times on the way up to L and D.
The nurses tried to make me lay flat and hook me up to the belt monitor, which was EXCRUCIATING, I kept it on for a minute and then tore it off, which really ticked off the staff, but I was way beyond caring at that point. I refused to lay flat and stayed standing, bearing against the bed or dd's father. They let me get in the tub, which was instant relief. I had a minute where I thought "I could really use those drugs now" but had made a "deal" w/ my support person that if I said that, for her to make me wait 15 mins (I highly recommend this "deal" too because by the time those 15 mins have passed, the baby is probably really close to birth). I was in the tub only maybe 5 or 10 minutes when I saw blood and felt like I NEEDED to push. I *mistakenly* whispered that out loud, and then all panic ensued and they made me get out of the water (this hossy won't allow water birth, just water labor).
The b**** nurse kept trying to force me flat on my back, and I kept saying NO (coz it hurt SOOO much worse to be on my back!) and I'm demanding to be on my knees bearing down on the back of the bed. For some reason this lady was STUCK on the idea of "checking me" and breaking my water (dd was coming down "in the caul" or whatever, coming down along with the bag) and kept stabbing her fingernails into the bag. She was really horrible and having to fight that nurse was the worst part of the whole experience.
At this point, I'm screaming, WHERE'S MY MIDWIFE? WHERE'S MY SISTER? because I don't have the energy to fight with this nurse anymore (I'm telling her I feel dd's head coming down and she's telling me no, no you have a lot longer to go, yeah right). Well, finally this nurse and I "compromised" and I turned sideways onto one leg---for some reason she "couldn't" check me on hands and knees. I realize now that she should've just left me the h*** alone!
But anyways, the nurse popped my bag of waters and dd's head starts to present, at which point my mw arrives in just enough time to literally throw down her keys and "catch" my little bundle right at 6:13 pm! I was at the hospital less than a half hour when she was born.
It was awesome! I felt like such a roaring, victorious goddess! And even though I was induced, I don't think I could possibly have labored and birthed more "naturally" than I did.
I recommend staying home as long as you can, if they'll let you go home to labor after the induction. That is what made the experience so natural for me; I was totally un-inhibited and arrived at the hospital with just enough time for the birth.
If you can't go home to labor, then try to make the space as "yours" as you can, and definitely have someone willing to advocate for you so that you're not doing staff-battle as you're in the final throes. You don't have to have the drugs just coz you're being induced. If you can go outside and walk around, do that as long as possible!
This can be awesome! You can still make this a rockin, memorable experience! Don't for a second bat an eyelash if someone makes you feel like you're not having "natural" labor---that is all semantics. Even Ina May talks about using sex, nipple stimulation, or castor oil to get the labor process going, and no one would say that she's not an advocate of natural labor!
Maybe you and your partner can "induce" at home w/ other methods before your induction date in order to maintain a little more of the privacy that you desired with your planned homebirth.
And FWIW, as I have no basis for comparison (yet) the induced ctx were not unbearable or 10x worse than "natural" ctx. You can still breathe/work through them. You can still use counterpressure and staying vertical to cope. Don't lay flat! Don't let the hossy staff boss you around! You just stay inside yourself and be as un-inhibited and loud and even bitchy if you have to be. This is YOUR experience and no one can take that from you---even if you have to be induced and birth at the hospital.
I am wishing you well! This got way more in depth than I thought it would.

I am on your side here! pm me if you need more support---wishing you and your family an awesome birth experience!