Over the last year or so, I've increased the pressure I use to strop. Mainly when I first lay the razor on my linen and leather. I do lighten up some as I go. No real reason, it just happens. I started and stayed at feather light for years and one day got frustrated with a wedge, stropped the bejesus out of it with heavier pressure and boom, awesome shave. Super thin grinds are a different story, but I only have a couple of those.
But, that's just me. If you have success with that light of stropping maybe a durable foam pad under the stropping materials is all you need. I still suggest foam or somesuch, just to compensate for inconsistent thickness in leather. On the other hand, my father still uses that dang stiff paddle and it works for him, as well as others.
Maybe it's just not my cup of tea...