I have read that you can use the high limit thermostat (3390291) in place of the thermal cutoff (3398671). We never leave our dryer unattended so if this is safe I would be happy to do it until our replacement thermal cutoff is received.

I do not understand why you would do that.
Especially when it could burn your house down.

The fuse is an additional safety for the hi-limit which is also a safety device.
If the hi-limit's contacts weld together keeping the heater on all the time then the fuse blows.
Also if the heating coil should ground and then the hi-limit or main thermostat cannot control it then the fuse blows.

So if you have a dryer fire which burns your house down and the insurance company found out that you did this they could say that you are not covered.

If you have a problem with fuses blowing then you have to find the cause.
The hi-limit should regulate the heater so that the fuse does not blow.
Eventually if the unit is running off of the hi-limit it's contacts will weld together.
That is why they include both in the kit, they assume that the hi-limit did not do it's job and is no good.
This is not always true as a grounded element can blow fuses as neither thermostat can control the heater.