You could take an Uber or Bolt to Windsor. It's about a 25 minute drive or go into Central London via tube or train (about the same time). As mentioned above you are at the hands of TFL going into London. Any number of disruptions could derail your plans.

Going landslide is pretty simple and painless. With US Passports you use the EGates (just make sure you all have the newly required visa.)

Going back into T5 is relatively painless also especially if you have OneWorld status and can use the First Wing.

Also as mentioned there is a Sofitel attached to T5 but you need to go landslide to access. Personally don't think it's worth it just to get some rest.