The EMI seems to be nothing . . . but a few years ago I found the
range burners were causing my computer modem to slow way down due to
EMI. Took me years to figure out the stove was causing the problem .
. . but I built a common mode filter for the incoming power (all 20+
amps or so). The filter is still in there.

It wouldn't be the first time the mechanical range controls shorted
and caused the burner to stay full on, so the triac is no worse in
that respect.

The idea that the triac, just sitting there, could decide to short has
me worried too. I have a lamp dimmer in my bedroom that is one of
those push on/off. I leave it on, and just turn it down all the way
and it hasn't shorted in 20 years.

But there's more to lose if the range shorts so I want a double
make/break switch for that.
--

The mechanical controls have no temperature feedback either, it's all open
loop.

You'll definitely want a mechanical power switch prior to the triac that
switches both sides.