How can I control my furnace blower independently from the furnace itself?
To accomplish this, you can use a 2-stage thermostat. You'd connect only the 2nd stage to your furnace. Both stages run the blower.

When the temperature drops to say 69, the first stage will start your blower. When the temperature drops to an even lower temperature, the furnace (stage 2) will be switched on just as you describe.

There are many thermostats which can accomplish this. Here's a great video I found
which demonstrates how a 2 stage thermostat works. You can see that the first stage is activated when the temperature is slightly lower than the set temperature and the second stage is activated when the room temperature is much lower than the set temperature. There are dials to set when the second stage is activated. He also shows the wiring for the stages. In your application, you'd leave w₁ unconnected and connect your furnace to w₂.