[I moved this to the Adventuron category.]
As far as I know, your history is stored in the browser’s cache.
You can use the Page Up/Page Down keys or the mouse wheel to scroll up and down through your recent history, but this is obliterated when you move to a new room or type LOOK.
You can use TSTART to start a transcript and TSTOP to stop it, but it doesn’t prompt for a file name until you stop it. If it’s really that important to you, you can use this each time you want to refer to the file.
I don’t think you should ditch Adventuron just because it doesn’t have full on-screen scrollback, as very few systems have this. It’s actually the interpreter that provides this feature, not the engine. If you ditch Adventuron, you’ll be missing out on some very good games.