Strayhorn's way to winning is through reaching those Republicans who are disaffected with Perry, but more importantly getting Independents and Democrats to vote in the Republican primary. Texas has no party registration and at the beginning of each year you can change which party you vote in their primary (this is how John McCain came so close to defeating George Bush in the Republican primary of 2000).
You can't sign Friedman's petition if you vote in the primary. This could hold down deliberate cross-overs in the GOP primary, especially from the Austin area (Strayhorn was mayor). For the hardcore Dems, there is likely to be a primary for governor.
In 2000: Bush 87.5%, McCain 7.1%, Keyes 3.9%.
I think the press has been boycotting her since Katrina. On the Sunday before Katrina hit, she announced that she was suspending campaigning. On Wednesday, when the evacuees started coming to Texas, she issued a press release attacking Perry's inaction against child molestors.