The best solution is probably to customize the weather script (it’s written in Python) and host it on your own server somewhere (it can even by a Raspberry Pi sitting at your home). But this does require re-compiling the firmware because the weather script location is currently hard coded and cannot be modified through the web interface.
Another workaround is to use two programs to simulate what you need: one program is set to start, say at 8am, with 6 minutes of water time (i.e. your minimum), set ‘use weather’ to ‘off’; the second program is set start after the first program finishes (e.g. 8:06), and 6 minutes of water time as well, but ‘use weather’ is enabled. The overall effect of the two programs is that you have a minimum of 6 minutes of water time, average of 12 minutes of water time (assuming watering percentage is 100%), and a maximum of 21 minutes of water time (6 + 6 * 250%).