Okay, so all my lodging is now booked. Itinerary has been updated to reflect changes with rental car.
UPDATED ITINERARY
Day 1: Arrive in London early morning (MSP non-stop to LHR). Take tube from Heathrow to Waterloo via Piccadilly (I decided against the long walk). š Stay 5 nights in London (daily itinerary TBD)
Day 6: Train to Plymouth. Spend 1 night at Premier Inn Derry's Cross, then pick up rental car at Europcar office on Day 7 and drive to Royal Duchy Hotel in Falmouth. Stay 4 nights and explore Cornwall.
Day 11: Drive to Grosvenor Hotel in Plymouth. Stay 4 nights and explore Devon. Return rental car on Day 14 in Plymouth.
Day 15: Take train from Plymouth to Liverpool. Stay with friend for 3 nights.
Day 18: Pick up rental car in Liverpool and drive to Bulls Head Inn in Castleton. Stay 5 nights and explore The Peak District.
Day 23: Drive to Foxglove Cottage, Laskill in Helmsley, North Yorkshire. Stay 7 nights and explore York, Yorkshire Dales and North Yorkshire.
Note: Here is where I deviated from everyone's advice about splitting up my stays in this area. I got such a good deal with this cottage (it averages out to around Ā£70 per night) that I couldn't resist. It's a full self-catering cottage with a washer and all accoutrements. I know it means I will be driving more, but that's what I do here at home. I live so far out that I have to drive 20+ minutes to get anywhere. So it doesn't bother me to have to drive a bit more.
Day 30: Drive to the The Bakehouse B&B in Seahouses. Stay 3 nights and explore Northumberland.
Day 33: Drive to The Old School House in Haltwhistle. Stay 3 nights and explore Hadrian's Wall.
Day 36: Turn in rental car in Carlisle and take train to Oxford. Stay one night at Marriott Courtyard Oxford City Centre and explore Oxford.
Day 37: Explore Oxford in morning and early afternoon. Take Airline bus to Heathrow. Check in at Holiday Inn Express Terminal 4. Relax.
Day 38: Get up at an ungodly hour and head to airport. Fly LHR-->AMS-->MSP. Cheers, England!
UPDATE: PROBLEMS SOLVED: I am picking up (and dropping off) the first rental car in Plymouth (using AutoEurope/Europcar), then will pick up my Arnold Clark car in Liverpool, and drop off in Carlisle.