That is the correct list for the OpenSprinkler. The OSPi interval program available on the Raspberry Pi has an additional option as you mentioned, rp. It also accepts custom commands set in ospi_addon.py.
This is a sample homepage result:
You can get the variables you are after using the following regex in PHP (the regex can of course be used in any PCRE programming language):
preg_match_all("/(ver|devt|nbrd|tz|en|rd|rs|mm|rdst|mas|urs|wl|ipas)=[w|d|."]+/", $data, $matches);
In this example, $data is a string holding the home page result as shown above.
Hope this helps.
Update: I don’t think there is an easy way to get the next run-time without cycling days in preview mode and finding matches. Probably not very difficult but could be slow assuming your next run time is days/weeks in the future.