Spartana, my mother did almost a year of slow travel about 8 years ago immediately following her retirement. She only had a U.S. Passport, so was not able to take advantage of a U.K. Passport but I'll share how she handled things. She spent the first 90 days in the Schengen zone, no questions asked upon entry from the U.S. Then, at that time, Croatia was not part of the Schengen (I know they applied - not sure whether they are now or not), so following her 90 days in the Schengen she went to Split, Croatia (ended up being one of her favorite places) and stayed in a beachfront studio apartment for a month. Thereafter, she went to the U.K. for 90-days. Upon entry to the U.K., they demanded to see proof of her exit plans. She had not purchased a return flight to the U.S. yet but they accepted proof of her booked accommodations following her time in the U.K. She was firmly told to not stay in the U.K. beyond 90 days.
After her time in the U.K. was up, she took the chunnel to Paris and began another 90-days in the Schengen all over again. She had been out for 120 days at that point, so was well within the 90 out of 180 day rule. She returned home after completing that stay.
She did not stay in hostels. She rented studio apartments through Airbnb or Vrbo - obviously we were quite careful about making sure places had a sizable number of reviews before booking and she had criteria as far as laundry facilities, kitchenette, private bathroom, etc. We pre-booked everything well in advance, which meant she was usually booked for a place 90-120 days out. This may not be as spontaneous as you'd like, but it worked very well for her.
Her budget for monthly lodging was $1500 and this ended up ranging anywhere from $500 for the month in Croatia, to over $2,000/month for her time in London, but overall she stayed within the $1,500/month average for lodging. At the time of this trip, the Euro & Pound were both much for expensive than they are now. This was all pre-Covid and I know rates have gone up, but I also know you can do it for less than what my mom paid. Her entire budget for the year was $30K and she was able to stay within that budget.
You're well traveled and I know you can figure all this out, but if there are any questions you have that I might be able to help with, please feel free to reach out. I was the travel planner extraordinaire for her trip and, honestly, it's quite a bit of fun to live vicariously through others! You are going to have a fantastic trip.