The gemara in the 3rd perek of shabbat has a big sugya about the whole issue (whether the mishna there that talks about removing or covering the coals is talking about shehiyah or chazarah), and is in the end inconclusive. The rishonim rule on this in various ways, but it sticks out in my head that the Rosh rules leniently (that shehiyah is allowed, and the mishna is only talking about chazarah).
The Mechaber brings a stam and a yesh omrim. The stam halacha is that shehiyah is not allowed unless the coals are removed or covered, but the yesh omrim is that the shehiyah is allowed. There's a general rule in the Shulchan Aruch that between a stam and a yesh omrim the halacha is like the stam, but Sephardi acharonim spill a lot of ink explaining why the halacha in this particular case follows the yesh omrim.
The Rema, on the other hand says outright that the minhag for Ashkenazim is to rely on the yesh omrim.
So I don't really see why you want make a distinction between gas stoves and coals. If you're machmir not to leave food on the stove without a blech, it's just that: a chumra, even with coals. If you're looking for grounds to be meikil, there's grounds even with coals.