Try an offset seat post, that will help get your seat back a little further.
Other than that, sure, a different seat tube angle would change the spatial relationship between your rear and your feet. But that angle doesn't change too much between the various road bike frames.
Perhaps shortening the effective top-tube length (forcing you more upright) might help the feeling - you can get a shorter stem, or different handlebars.
It begs the question - why do you care where your feet hit? If the current scenario is comfortable, then why change it? Unicyclists (mountain at least) ride with the pedal just in front of their heel.
Given your shoe size (58-59), I can imagine your feet are hitting the front wheel when you turn sharply - so maybe that's the reason... On some bikes I have that problem, and I wear only 48.
More drastic changes could be switching seat types, like a banana seat (yes, you might look silly). Or switching bicycle styles, say to a recumbent.
But, really, if the change doesn't "feel" right, have you tried it for an extended period of time? I'm thinking a couple hours (cumulative) - to get past the initial reaction. Maybe you've just been riding mid-foot so long it will take a while to change what feels comfortable.