Propane can be more expensive than oil once btu content is considered.
There are gas conversion burners for oil furnaces but it would be far better to just put a new condensing furnace which would be more efficient and safer if you decide to convert.
Converting likely won't save you any money.
Oil burning furnaces need to be tuned to run at rated efficiency - I would start there. They need more maintenance than gas.
While oil is expensive, it's possible your fuel bills are high due to having a furnace that's far too large for the house. When the cycles are short the furnace doesn't come close to hitting rated efficiency, especially an oil one with a thick heat exchanger.
It may be possible to de-rate the furnace. Can have a smaller nozzel put in, the fuel to air mix gets adjusted and the fan slowed down.
If you have reasonably priced electricity, you can look into adding a heatpump to carry the heating load in milder winter weather. Heatpumps supply 2 to 3+ units of heat for every unit of electricity consumed so you can save compared to oil/propane.
When it's too cold for it to keep up the thermostat automatically makes the switch. Best way to do this is with a stat the uses an outdoor temperature sensor - heatpump gets locked out when it's too cold.
Beyond that, focus on the house - does it have a crawl space? Ducts in unconditioned space? Ventilated crawlspaces can increase heating costs. Attic may need air sealing and like u brought up more insulation.