I'm not Laura, but I hope you don't mind me chiming in.
The Tube, Overground and mainline rail all work together. Other than the Elizabeth Line (new name for Crossrail1 to open in a year or 10) and Thameslink, mainline trains don't enter central London and are interconnected by tube lines and buses. You can't get across without 'em, not unless you're rich and run to taxis.
Croydon is an interesting choice of a base. Do you know about Croydon? I spent several years in South Croydon when I was young and Croydon has changed beyond recognition - not for the better. You may have heard of the London fires and riots a couple of summers ago. That wasn't in tourist London - it was in Croydon.
But the borough of Croydon is large. Maybe you have found a great place. But if you do have a place away from the train then you need a way into London.
Commuter trains from the area around Croydon are basket cases. Between the reconstruction of London Bridge station and the reconstruction of the tube at Victoria it is even worse because most of the trains from East Croydon go into either London Bridge or Victoria. Those trains have always overflowed as long as I can remember, and more people than ever are on the train.
That isn't to sound all doom and gloom but I want you to be aware.
Have you measured the times of your train connections?
Are your "X"'s nights or days? To get a full day you need two nights.