You mentioned kitchen counter push-ups... that's incline push-ups, which are easier for starters. But if the counter is too high, you might not be using your core much... try a lower spot like a table edge. Keeping your body straight helps with the calm feeling. I learned that when my back got sore... tweaking the height fixed it. So maybe check your form.
Yeah, tweaking the height like you said fixed my back pain too. I moved to a lower surface and felt my core working more. Now I make sure to keep my body straight and it's much better, lol.