You are wasting your time and money trying to change away your electric cooktop for cost reasons. The only sound justification would be "I want gas".
Why?
Cost per BTU delivered to your cooking pot.
Propane costs in your area about $2.14/ gallon, if bought in bulk (So much cheaper than here in NJ!)
http://www.eia.gov/dnav/pet/pet_pri_wfr_dcus_STX_w.htmA gallon of propane contains 91,547 BTU. So your cost per raw 100,000 btu is $2.338
Lets assume the worst marginal electric rate for your area, $0.165 per kWh (You are probably paying significantly less)
https://austinenergy.com/There is 3412 BTU in a kWh. Your cost per raw 100,000 btu is $4.86.
So it looks at first like of course you should go propane! But wait.
Without getting too in depth, electric burners are more efficient at putting that heat into your pan than a gas burner. A gas burner can throw more BTU at the problem, but you pay for them. Lets say the electric coil burner is 75% efficient at getting heat into your pan, and your gas burner would be about 40%.
https://www.centurylife.org/is-induction-more-efficient-than-electric-coil-or-gas-an-energy-efficiency-comparison-between-stoves/Now the cost per 100k BTU delivered to your cooking is:
Propane: $2.338/.4 = $5.845
Electric coil: $4.86/.75=$6.48
Thats a much smaller difference. Now you have to account for the payback period of your investment ($300 you said). We'll assume your time to shop and install the new unit is free. Same with your time to refill your propane, and that somehow you get it at the bulk residential price rather than the inflated cost charged for smaller portable containers. Also, you get a magical deal where the $300 is financed at zero cost, you just write a check for the energy savings difference every month until it is paid off (basically, no interest charge or opportunity cost to deal with).
The payback still does not happen until 47 million, 200 thousand BTU have been delivered to your cooking work, or about $3058 in total costs later.
The department of energy estimates that the typical user of an all electric range (stove+oven) uses 58 kWh a month of electricity for their electric range. Going back to the rates I assumed for you, the payback is then 320 months of usage, or 26 and a half years.
26.5 years to get back the $300 spent for the propane gas cooking range.
There is also the air conditioning question. Since you are putting more energy in when using propane, despite the energy being cheaper, you will heat up your home more. Because it is a flame heating the space, you will also need to ventilate more, and the flame makes humidity. So, your air conditioner will have to work harder than with electric cooking.
I made the numbers about as generous as I could in favor of the propane. Bottom line, it almost always pays to keep using a functional and paid for appliance. My rental home has an oil fired boiler for heat, dating back to the 1950s. About as inefficient as it gets, and oil is sometimes very expensive (not this year). Here is the mid atlantic, winter can be cold enough to get expensive in an old house. Even there, the payback to switch to gas is in the 10 year range, well outside of the time I plan to live here.
As to your questions of safety and legality... you can count on it being against fire code. Propane sinks, so in a fixed structure tends to accumulate in the low spaces like crawlspaces and basements. Propane tanks outside the house (usually a set distance away, for fire reasons) are legal. Indoors? Don't count on it. Mobile homes and RVs get an easier pass on this from safety perspective, as they tend to be elevated above the ground and the propane dissipates more readily as it sinks out of the structure. Electric is hands down safer than a gas range of any sort. Gas cooking affects indoor air quality to a greater extent than electric, since it is using air to burn. You will be turning the oxygen in your indoor air into carbon dioxide, humidity, and a bit of carbon monoxide and other trace gases.
