I was able to easily peel off the weld spots with my fingers. Not acceptable!
Yep - that is a similar outcome I am having, and a sign to stop and reevaluate what method(s) I will be using...
@Zambam how well did the 304 to Cu single layer bond?
As silly as this analogy might be, my gut reaction... is make it like I make my sandwiches. That is, I like having lots of interlayers of flavor vs relatively thicker layers of each ingredient. Ya know, spread out the flavors

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The problem with adapting that analogy back to the metal sandwich is it probably necessitates a much thinner layer where the resistive heat forms to create the weld bond.
Maybe something like ~0.05mm thickness 304-Fe ribbon on top of and between two layers of 0.1-0.15mm Cu ribbon? That way, the resistive material is thin enough to not block penetration of the weld through the Cu, yet simultaneously able to maintain enough resistance for heat to securely bond the Cu. E.g. this might better distribute the heat throughout the entire thickness, rather than being 'top heavy'?
Another idea on this, instead of side by side placement of the weld probes on the same face using the infinity slot gap technique, I'm pondering experimenting (when I get off work this week) with orientating the material vertically on the workbench, and placing the welding tips on either side, e.g. the probe tips representing the metal sandwiches 'bread'. This would seem to me, to be more like a traditional alligator style tack/spot welder, that is, the ones I remember using in shop class 20+ years ago... Would this work I wonder?