I agree with the pps, that fear is not a good way to go into birth, so it may be better to find another hospital.
That being said, there were points you brought up that are easy enough to work through.
For some of the more practical things...
The mess. There really wasn't one for us. The only "mess" we had to deal with after the MWs packed up and left was the kitchen (which is always a mess). The MWs packed up all the garbage, and had a hamper for the laundry, etc., so none of it needed to be "dealt" with. They volunteered to start the laundry, but since I hadn't walked them through it beforehand I wasn't comfortable with them doing that. But that was MY hangup.
Birth tub. If it's such a big concern, don't get one. Personally I didn't find it helpful at all. I spent a LOT of time in the shower, but the tub didn't help. I'm still debating whether I'm even going to bother with one this time. If you WANT one though, go to a hardware store, pick up some painters tarps, the plastic ones AND the cloth ones. Put down the plastic, then the cloth, then the tub. We did that on our 50 yr old hardwood floors and didn't have ANY problem. Have a stack of towels (or a laundry basket of them) next to the tub. As for where, anywhere you could fit a kitchen table. Do a test run beforehand to be sure the tub doesn't leak. If you're careful filling it and the tarp winds up wet, you know you have a problem. But since you're not in labor, you have time to deal with it.
As for the pain... that's a totally individual thing. But I'll say that the IDEA of running a 5k makes me want to curl up in a ball. But I spent 5 days in labor with DS. I didn't ask for drugs until I hit transition, by which point it was too late. I'm not going to say it didn't suck, but it was a completely different kind of pain than anything else I've ever experienced (including DS1's birth, which was a hospital induction). If I had known going in that it was going to be 5 days, I never would have agreed to a HB, but from this side of it, I'm glad I did, because I learned something about myself. And the fact is that if you're in a long labor, and you get to the point where you just can't deal any more, then transferring to the hospital for pain relief is always an option. In fact, that's what most HB transfers wind up being for - not emergent reasons.
As for the family - there are lots of things that can be done there. Not announcing the birth until afterwards (like the next day, or more). Spelling it out plainly that you will be seeing visitors on X day between Y and Z times only. A note on the door that details the baby's info and asks visitors to go away until visiting hours. Disable the doorbell. Changing voicemail to something similar, turn off the ringer. Setting up a schedule beforehand with family - you're going to need help with XY and Z. Who's willing to come over and help out with these things? This is one I'm doing this time, specifically in regards to DS, working up a schedule with all the family to come over one at a time and take him for a few hours so he doesn't feel left out of the attention. Have you discussed a meal train with anyone? That's another good way to do it. I know many MWs who post a note on the door when they leave to the extent of "new family needs bonding time, please limit visits to 15 minutes and do a chore while you're here" - a list of chores on the fridge is really helpful so you don't have to stop and think about what might need doing. And if all else fails, stay in your bathrobe/pjs, and put on your most imperious attitude - don't get up to do anything for anyone, including yourself. Make yourself a throne and stay there (with baby). Wearing baby skin-to-skin in something like a Moby is also really helpful for this. Just remember that your/baby's needs overrule everyone else at this time. Hurt feelings, guilt trips, etc., don't matter one whit.