On flaps and stall speeds, for heavy jets, we almost invariably have LE devices of some sort, slats (Airbus, B737 outer, B757,767, 777, 787), Kruegers (B737 inboard, B727), flexible Kruegers (B747). If the wing is relatively straight, you can get away with simplified systems of TE flaps only, but the LE is normally a fairly healthy radius to give a benign stall, and there is a need for some additional twist if the wing is swept, or some span wise flow control like fences, vortilons, VG's etc. A good read on the subject is:
Rudolph, P. K. C. (1996).
High-Lift Systems on Commercial Subsonic Airliners. NASA Contractor Report 4746 (Issue September).
https://doi.org/NASA Contractor Report 4746. Bottom line is the slats on our heavy jets are very good at their job, which is to improve stall behaviour, reduce stall speed through much higher CL/AOA. Most heavies will schedule an auto slat extension at high AOA when the wing is clean, a swept wing that doesn't do that, or that it occurs with some asymmetry will give a really good roll off at the stall break. Flaps are part span on most aircraft, slats, and slats/kruegers are effectively full span. High performance TE flaps that are multi element, and increase surface area will produce a fairly good stall speed reduction, but it is still pretty limited in the extent of change. The flaps only configuration increases the inboard CL for a given attitude, by both increasing the camber of the section, and the AOA, but as the overall lift is affected by the component CL of the total wing, keeping the inboard section below stall AOA means the outboard section loses AOA and therefore CL, but this gives better lateral control authority so is tolerable.
Flap behaviour can be enhanced, guys like James Ross at NASA Ames (nowadays "Jim"), John C Lin at NASA HQ and many others have worked on many different mechanisms to improve foil performance.