some thoughts
considering Europe is still a large area, and there are always waves of pilots nearing retirement?
yes, its large but languages continue to be a barrier, even in an english driven profession as pilots. do you speak german/french/spanish/dutch?
mainline lufthansa/AF+KLM/Iberia require local language.
what about Ryanair or easyjet? - not really for people with a frozen ATP and no time on type. you need to go to one of their training programs. really encourage you to check their websites.
You also mentioned the integrated schemes most airlines use to recruit-is there no hope for any of us who've done either the modular/integrated approach at a flight school with no airline recruitment affiliation?
i cant add much to the general integrated vs. modular debate. a big picture insight however is that recruitment in the EU does NOT work like in the US.
its NOT PPL->IR->CFI->Regional->Mainline
instead its Nothing->pass some kind of selection -> Flight school that probably but not definitely offers employment -> mainline.
there is always luck. get a nice corporate gig through connections.
some companies do have different training approaches and want ready entry FOs.
but the chances are smaller than getting a regional job. (or instruct first to get hours)
that uses your current skills and at least a little bit of earning power. you can try the ATP via DL. it will take longer and will be very frustrating. but you get the same options to be in europe whilst keeping your US options open.
im not sure what is driving your desire/requirement to go back to europe but i think a more gradual transition has less risk involved. (whilst you learn more about how it works in europe).