So some materials it is hard to break a chip, might try a deeper DOC, certainly your feed is up there. The 1340GT is a fine machine, but you start getting into rigidity issues if trying to push it much harder. Also insert type and style play a large factor. I typically used CCMT tooling for steel/SS and my WNMG for aluminum and softer materials. You should look at your SFM and insert recommendations. I have done some machining of 4140 and 8620, but primarily with CCMT 32.51 insert made by Iscar (IC907) covers a wide range.
On 416 SS, I did check some other recommendations and you are in the ball park, this was for barrel work so assume around 1" diameter. Your feed rate is where I would wnat to be for SS, but may need a bit more DOC. On finish work I would switch to my WNMG with a sharp ground edge (Korloy insert). See attached document with various inserts (that worked for me on the same lathe). Final pass is often done with a ground sharp edge, DCGT or WNMG at a lower feed. DOC is often dictated by the nose radius and sharpness of the insert edge to achieve cutting as opposed to pushing the material out of the way.
SS 416
CCMT09T304HF (Iscar IC907) in a 5/8 inch SCLC holder, 800 rpm, Feed of .008/rev, DOC 0.03"
CNMG431 F3P (Iscar IC8250) Feed of .007/rev CSS 725 DOC, .070"
Iscar Sumo Tec WNMG inserts. Specifically WNMG 080408-M3M
Seco TP2500 or TP2501, TM2000 with the MF4 chipbreaker
Cactus Tools sells a lot inserts/machine tooling on eBay may be worth emailing them to see what they recommend. This insert may be worth trying for rough/bulk material removal, note the nose diameter. Then switch to a ground edge for finishing.
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416R SS and 4140 CM with carbide inserts
Tennon Turning and Facing with Indexable Insert Tools and Carbide 800 rpm
Feed of .007" for Rough and .002" for final pass
4140 recommendations, the DOC is not achievable with a smaller lathe and I would use cutting speed and feeds similar to 416 maybe with a slightly lower SFM.