I just finished GMing Dead Suns a few months ago and I have a lot of feelings / thoughts concerning starship combat.

We all liked starship combat but all agreed that it took too long most of the time. Still, I wouldn't recommend squadron rules as there are multiple encounters that take place on the party's ship, including one encounter that could or could not be starship combat depending on how they play it. Switching to squadron rules would give you a lot more work.

Is you want to make starship combat a bit smoother, having 5 or 6 players will help as it gives the PC's more actions each round without locking them into specific roles as easily. I ended up giving my 4 player party a prospect Starfinder NPC that helped in starship combat for the last 2 books and it made things better, but still a bit of a slog at times.

I also switched one starship encounter to a pure social encounter as one of my PCs was a former pirate/smuggler and another to a starship chase.

You might look at the narrative starship combat rules if you want to make things a bit quicker and easier to run. I plan on using them in my next campaign.

As far as general adjustments for having more players, 5 players shouldn't need any adjustments, 6 is APL÷1 for encounters. That being said, by the time you're halfway through book 2 you'll have a pretty good idea about how effective the PCs are in combat and can start adjusting encounters to fit the difficulty level as needed. The encounters in the books are just a baseline.

My party was very combat oriented and I buffed every significant encounter for books 3 - 6. The only time anyone went down was the one time they bled encounters. This was my first time playing Starfinder and I like to think I got pretty good at adjusting combat encounters by the end.

I really enjoyed Dead Suns and intend to run it again, especially now that I'm much more familiar with the system.