I'm not reading all three pages of posts but from skimming though I'm not seeing many serious answers to the original question.

"How much does a turret press increase your output over a single stage, all thing considered. i.e. changing calibers and making adjustments as well as better production."

Honest answer, it depends on the turret setup which depends on options available to each brand. The reason the Lee Classic Turret is mentioned so much is it has the most going on compared to the rest. The RCBS, Lyman, and Redding turrets are all nearly clones of each other in function. You can sort of easily swap turrets on them so doing a caliber change is easy enough but not as easy as the Lee. You can prime on the press for all of them but again I feel like Lee wins with ease of refilling primers. You can drop powder on the press of any of them but once again Lee's dies can auto drop the powder for you with their powder measures. So it's not so much the number of times you pull the lever so much as it's the consolidation of efforts. Single stage you have to break most of it up and you most certainly have to touch the case over and over again. With the turret you save that bit of time with setting the case and just going through the turrets motions until you have a completed cartridge in front of you. And with the Lee version being auto indexing you don't even have to manually rotate to the next station. So how much time to do save? Obviously not as much moving from single stage to progressive but it's significant enough that I feel like it was worth it and don't begin to regret the purchase.

Adjustments to the dies is I feel like another huge win for Lee. The adjustments are done with your fingers instead of tools. And after many years now of use they still work as well as the day I bought them. FYI if you do buy the Lee turret then you can use any brand dies but you may need to buy Lee's lock rings as the rings need to be small enough to fit the turret.

Better production? As in more output or better product? You will definitely make more ammo in a shorter amount of time than a single stage. Better product, I think you will make the same quality as you would a single stage. I will say the Redding design (and I think the Lyman has this as well) has a non tilting turret so that may be the best of them but the Lee turret slightly lifts each time although it's the same exact amount each time. In theory, the Redding may be superior but you had better be using a micrometer on your targets to see the difference.

My Classic turret is still to this day my most used reloading press just because it's so easy to setup and get running. Heck, a caliber conversion takes longer to explain how it's done than to just do it. Bottom line, yes any turret will be significantly faster than single stage batch reloading and the Lee design offers the most ease of use with handy options that speed it up even more.