Staying near Heathrow for 16 day London trip?

I am planning a trip to London with a friend in early May for 16 days. We are both highly particular about hotels, and our dollar (Canadian dollar) is currently very weak compared to the British pound (about $1.80 CAD to £1 GPB).

Many hotels in central London don't seem to have two beds, or the rooms with two beds are much more expensive. To save money and ensure the room is a decent size with two beds, we're considering staying at the Renaissance Hotel at Heathrow. This would be about a 45 minute-1 hour commute into the city each day. The room would be £123 per night, including breakfast for two, so £1,972.00 GBP, or $3,485.96 CAD, total for the trip.

Google Maps shows that there's a bus line a two minute walk from the hotel that will take us to the Elizabeth line and from there into Central London. This would cost between £5-£6 each way for each of us (bus fare + tube fare).

Does this make sense to do? Our itinerary is all over the city; we have one day planned at the Tower of London, one day for St. Paul's/Shakespeare's Globe, two days in Covent Garden, three days in Westminster, one day in Camden Town, one day in Notting Hill/Kensington, and one day in Canary Wharf. We are also planning to do one day at Windsor Castle, one day at Hampton Court, one day at Hever Castle, and one day at the Harry Potter Studio Tour. And we are planning to see probably 5-6 West End shows.

We figured that given that our itinerary is all over the city, we'd end up on transit a lot anyway, and the amount of travel time we'd save staying more centrally would not be proportionate to the increased cost (likely close to double the cost, given how particular we are about hotels and that we want the extra space). We are also Marriott Titanium members and therefore usually receive very good service and sometimes upgrades from Marriotts (including Renaissance properties), especially internationally; the Renaissance also has a club lounge we'd have access to with food, snacks, and drinks.

We'd prefer to stay at a Marriott brand hotel, but the Marriotts located more centrally are either double the price or extremely small (we were looking at the Moxy in Stratford, but it's £40 more and doesn't even have a wardrobe for us to hang clothes, which for a 16 day trip would not be ideal).

Does it make sense to stay at the Renaissance Heathrow given these circumstances? Our only concern is that we might be quite tired after a long day and getting back on the tube to the hotel, especially if we're seeing shows that don't finish until 10:30 or so. We wouldn't get back to the hotel until 11:30 or later in that case, and we don't want to be tired throughout our trip.