Ah OK. I've recently** switched to POSE running, but in my case I think I've ended up running rather like your desccriptiuon (I think POSE allows for a range of contact sequences, but anyway ... ). I've stuck with middish-range cushioned* shoes, rather than your trendy things, but I am interested in the various minimalist shoes.
That knackered-calves feeling is exactly what I got the last time I restarted running after months of just cycling. I'm lighter than you, and managed a cautions 15mins (which is hopefully more than 1k!). Calves still ached like billy-o afterward, and I'd barely got out of breath.
* (I haven't read a convincing explanation of why cushioned shoes are actually _bad_ for you with POSE, so I'll stick with the shoes that fit me for now).
** (2 years but very few miles.)