What’s the best way to deal with skepticism from your software staff about an upcoming major change in their development process?

Change is tough for people , so when you update the process , there is an inertia that people have - It worked why are we doing this.
 When I have updated process , I usually tell a story along with why are we making changes, what is the advantage, what to we gain, how does it help the customer.  How does this impact you
I will include some key members in the transformation plan and give them some responsibilities and make them champions.
Keep the communication lines open, overcommunicate, and as you progress demonstrate the wins.
Lastly there will always be growing pains. We as leaders need to be patient , keep the target change and once the team has adapted.
I have taken the team through a couple such changes . It took a 1.5 - 3 months of complaining but finally we moved over the hump

Communicate the purpose clearly, involve the team early, provide training, and celebrate small wins. This builds trust, reduces resistance, and encourages ownership of the change.

I have guided many teams through major changes and the best way to do it is by getting them involved early and including them in the decisioning making process. When people feel included in the design they have skin in the game or become owners not renters. Additionally, accountability, consistency, and communication are key to success after the changes have been implemented. Holding all teammates accountable to changes ensure it becomes hardwired. Consistency in this context means to treat all teammates the same when implementing the change. No one gets a pass. Finally, there is no such thing as over communicating during major changes, not everyone understands every form of communication or learns at the same pace. Ensure your timeline allows for this learning curve. I hope this helps!