See the attachment for the wiring diagram..

[COLOR="Blue"]The heat will not shut off and subsequently blows the fuse.[/COLOR]
Just to be sure, is this the thermal fuse on the blower?
Often people also call the thermal cut-off on the heater a fuse.

[COLOR="Blue"]The heating element will shut off after turning off the dryer but only after it is manually stopped.[/COLOR]
I am assuming that this can be done by opening the door or turning the timer to off.
Does the heater stay off in air only?
Does low heat setting actually change the heat output?

[COLOR="Blue"]
Obviously the timer is an issue but I am unsure if this powering of the heating element / coil issue will be solved, yet, by replacing just the timer.[/COLOR]
I also doubt this is your problem as the timer cannot keep the heater on as even if Timer Switch 2 was shorted (contacts welded together) the cycling thermostat should regulate the heat.

You seem to have done a very thorough job of troubleshooting so I am also pretty well stumped.
Although the odds are very high I would check the new operating thermostat.
Hold it onto a stove element or heat it's face with a soldering gun to be sure that it will open.
If your oven temperature regulation is good then you could even put it in there to see if it does open at around 150 degrees F.

The thermal cut-off is a different kettle of fish.

Check all seals in the unit including drum and blower.
The reason is that the from the heater up to the blower the system is actually under a vacuum. If it sucks in room air then the cycling thermostat sees this and keeps the heater on.

Check the lint filter. Sometimes fabric softener residue can coat it reducing the air flow through the system. It should be cleaned with soap and water if coated.

[COLOR="Blue"]I have suspected the temp setting selector switch. The continuity tone on the meter on the low setting goes haywire before fizzling out. Symptoms do remain unchanged with the temp selector unplugged, as heater still stays on.[/COLOR]
I do not think it is in this area. In normal/high heat they are disconnected.
I am not sure about the fizzling out.

[COLOR="Blue"]I guess this works by the selector fooling the cycling thermo with a heater.[/COLOR]
Yes it adds heat to the thermostat so it thinks the unit is hotter than it actually is.

I seems strange that it keeps popping the thermal cut-off.
The hi-limit should prevent this. It should open at 225 while the thermal cut-off is at 350 degrees F.
One thing to note is that the hi-limit is just a safety with the thermal cut-off as an extra safety. So if it does start opening/closing it will not last very long.
Unlike the operating thermostat whose contacts are made to do this all the time.

I don't know if there is such a thing as a partially burn't out coil and it would not be getting hot enough, as well. i am at 10 ohms - enough to go over 360 - Make sense on the integrity seals

Thanks for the help.
When I arrived home this Sat afternoon, the new FSP timer had arrived.
***This solved the problem!

***We thank our God and Father of Jesus Christ and yourself for providing the way and help, of course.

After studying the schematic this week some I was becoming more confident (yes hoping) that the way the contact was broken T ~ W OR neutral was bypassing the cycling thermostat through the motor switches?
SEE SCHEMATIC timer switch 4.
So, I believe, since this would not stop making contact when it should on all cycles the white neutral actually became a direct "constant red"?

It is like a new unit. Every inch of this thing is clean. We have a new cycling thermostat on the blower box, thermal cut off "fuse" & high limit thermo on the heater. All FSP made in the USA. When it cycles is sounds nice and tight. Plus you can not hear the new timer running.

With the unit venting into the laundry room, no clothes in the dryer with the lint screen in place, cycling times are: 1) On the lowest setting - 70 (seventy) seconds 2) On the highest setting (or "roast 'em good") - 95 (ninety-five) seconds.

Next project: If you would like I will provide you with my research on the vent to out side booster vent fan options from FANTECH that I plan to install, next. This should ensure it keeps it well vented and reduces drying times, as well!

Thank You, Chris Huntsville, AL