Log in using SSH without password

Add -t to allocate a pty ... Ok, so now the user input can be seen, but I get Ctrl+H (^H) when backspace is pressed

Make your script run [ -t 0 ] && stty erase ^H and the Backspace key should be accepted.

An even better solution is to use a port of OpenSSH – for example, that from Cygwin or MinGW – it will give you full terminal emulation as PuTTY does, but keep it in the console window. (The plink tool is designed for raw 8-bit data transfers.)

Edit: A downside of Cygwin might be its lack of IPv6 support (if I remember correctly).

Get password prompt, cannot provide password like with plink

[...] but this is a closed, private network, and its easier not to bother with keys!

And yet you have a problem which setting up keys would solve :)

(I'll feel bad for saying this, but PuTTY also accepts -pw.)

You only have one user. So it's not a multiple users problem. Make sure the .ssh directory has mode 700.

However, you're doing it wrong anyway. You should create different users for each developer and put them in a common group. If they need to work on the same files, you make them writable by their common group and put them in a directory that has the "set group ID" flag set, so whatever they write to it will belong to the group.