Well, switching the ref is probably good enough, but... - You'll still potentially have an Voffset/RS resisdual current, unless you're adding one to ensure strict null current. I guess both are Ok though. - You'll need an SPDT switch, tied to the rail, etc... or need to switch all that upside down. (depends on your load) - That one uses one SOT23 against an SO8 at best for the other solution. - I do like simple solutions :-)
Yup, that's how it'll work. Just set the minus input additionnal divider so as to provide enough, but not way too much, additional bias. Just enough to ensure you slam the opamp output to the positive rail.
Recovery? Depending on your MOSFET, that's just 1 to 3V to slew. No big deal given your 1ms requirement. Any small 1MHZ GBW opamp should give you circa 1us settling time... Plenty enough.