A range that is 32 3/4" wide? That's a new one for me. So, I am guessing that you have a frame that is 32 3/4" wide with spaces (slots) for 3 (or maybe 6) modules.

There is no currently sold stove in North America that will fit those dimensions. The stovetops on "slide-in" ranges have cooktops that are wider than 30" in order to overhang/cover the counter, but those are only 31.25" to (possibly) 31.5" wide.

For a replacement range, all I can suggest is that you consider fabricating filler panels for the sides and and try to make them look like a design element that frames the stove and separates it from the countertops. The design mavens in the kitchens forum may be able to help, so you might try posting there.

If the 240v line to your existing stove has the electrical capacity (or if it would be easily upgraded), you might want to consider installing a cooktop and a wall oven in the stove space. You could have a frame fabricated to hold a 30" cooktop while filling the 32 3/4" space in front of the counter vent. (Maybe out of stainless steel.) Below that, you could build/have built a cabinet to more or less match the rest of your island and put a wall oven in the cabinet.

If you search here, you will find numbers of postings about set-ups for cooktops-over-ovens. Most of the recent threads are about doing this with induction cooktops rather than radiant electric ones, but the principles will be the same.

BTW, If you are going that route, have you considered induction?

As for the existing range wires: I'm not sure I understand what is fraying. Are you talking about wires inside the stove, the ones that connect to that problem coil unit or are you talking about the house wiring that is the power supply to the whole stove? If the former, is the insulation just a bit ragged that ends where it was stripped to connect to the coil or is it fraying elsewhere? If elsewhere, the stove is unsafe. If you are talking about the house wiring, it is time to get some re-wiring done. Cloth insulation deterioriates and (mostly) has not been used since the 1950s.