Perhaps I'm misunderstanding you but this tool expressly has a select and move tool.
I've just done a quick search and found one that I've not spotted before, which is a bit closer to what I want in that one respect, but not nearly complete overall (and not seen a check-in in 8 years): https://textik.com/ - that might illustrate the key difference that I see missing in asciiflow.
It's a shame that it's mac only.
Yeah, that looks to fit the bill nicely but is no use to me with my current mix of operating systems.