If your electric service is not overloaded, some form of permanently installed electric heat is nearly always the cheapest to install (without the "unattended space heater" issues), and the most expensive to run. If you wanted to redo the tiles (or it has none and you'd like to add them) an underfloor radiant grid would be nice, if you can ignore what it does to your electric bill. Otherwise plain old electric baseboard or a wall or ceiling radiant panel would work.
If cost to operate is an object, you might want to see if you can add to the duct feeding the laundry area and put a vent in the bathroom - or even relocate the laundry vent to the bathroom (if the heat will then flow back out of the bathroom in to the laundry area.) Ideally you'd want to consult with a heating professional to make sure that duct sizes and overall load on the furnace are OK, rather than just ripping into it and adding a duct. If you have gas heat, this will be anywhere from 1/2 - 1/4 the price of electric heat (depending on gas and electric rates.)
Next spring you should consider digging down outside that corner as far as you can manage, and installing XPS foam insulation sheets as far down as you can dig. Aboveground treatment will vary depending what your termite issues are - here we have little in the way of those, so it's OK to foam right up to the sill and stucco over it for appearances sake aboveground - in more termite prone areas I think you have to forgo the insulation between the ground and sill or it makes a place for termites to hide.
For a "creative" method you could make use of a hot water recirculation pump and run the return piping all around the walls or under the floor (thicker than an electric mat, though) or through a fan-coil unit to basically put the heating load onto your hot water heater, rather than the furnace - and you'd have hot water without the wait to boot.