I’d say go for it, or risk always wishing you had.
Working is difficult- most of the Europeans, Aussies and Kiwis who do the whole ‘gap year’ thing are on a Working Holiday Visa, but the US isn’t signed up for the scheme, and you’d be over the max age for them anyway. I stayed a year each in NZ and Australia on them.
There are ‘work for accommodation’ options, which don’t require a work visa, such as 'WWOOF, which, despite the name, and the description on the website, isn’t really just farming- I spent a week in a small pottery, for example, and stayed with some great people (as well as one lunatic, oh well…). Also a lot of hostels will do a work for a free bed scheme, informally, if you get desperate and are pretty reliable (I painted a room for a free week in one once).
Couchsurfing is also good, though flakes and the very odd do abound sometimes. If you’ve not really used it, there’s often groups for the area/city as well as individual listings, which you can join to get backup or emergency hosts. If you can, I’d suggest hosting a few people before you go, to get good reviews on there, and to get good current tips.
I would not get a car unless you do manage to get a job, and settle in one place for at least a few months. They’re great if you’re staying in one country, but if you’re crossing boundaries you can get into trouble with insurance and different requirements too easily. Besides, fuel is hella expensive over here. Consider liftsharing websites, if you’re not willing to go full on bum and hitchhike.
Oh, and if you wind up in the Southwest of England, PM me- I can’t guarantee I’ll have space, but I’m sure I can find someone who does! 