Is it possible to create a polyphonic synth in Eurorack. Yes. But you're reinventing the wheel in the most expensive manner possible. When you stated "pads" and by listening to your examples... I heard polyphonic sounds. Each voice has its own filter, VCA, and other elements. You'd have to reconstruct that in Eurorack, piece for piece with addition modules to handle things like routing pitch and gate to available oscillators, VCAs (possibly filters) etc.
You can definitely use Eurorack modules as part of an effects chain that you plug your hardware synths into. That's not any major issue between converting line level (hardware synth output) to Eurorack level (a lot hotter than your hardware synth). There are ways to sync your hardware synth to Eurorack and then modulate things in relation to the sequence as well.
My big point is to see if you can get where you want to go out of what you have rather than trying to make it work in Eurorack... which isn't a good fit for what you're wanting to do... as far as I can tell. There are lots of reasons to get into Eurorack. But it's a MONEY PIT... a sweet money pit... but still a money pit.