In 2016, Democrats did not try an alternative plan of picking up votes from the other side after they lost the November 2015 elections.
They might have tried except for the fact that their effort would have been futile. In current day Mississippi, politicians are not switching from the Republican Party to the Democratic Party. They may be in other parts of the country, but not Mississippi.
With no path to victory viable, Democrats did not even nominate an alternative to Gunn as speaker. Gunn was re-elected by acclamation. In a sense, Gunn had no opposition.
Still, in the current partisan political environment, it is not surprising nor improper that Gunn turned to fellow Republicans for his committee chairs.