First, you don't have a glow plug issue. Despite the WTS light at All times, once the engine has warmed-up they don't come on at all. So, any restart issues aren't related to the plugs or the relay.
Next, you need to know that not only will you get a WTS when you don't need to do any waiting (like when warmed-up) but, when really
cold, you should wait for much longer than it's on. That is, the Glow Plugs are actually running for Much longer than the light is lit. They're really not connected in any way...
On a 2000, look at the Tach when you're cranking it over and trying to start. Do you see the needle rising slightly? (you should or I'd be suspecting the CPS sensor).
You're having a "Hot Restart" issue and that's Much less common than all the COLD Starting issues you'll see as the weather turns. Don't confuse them
Usually, people have your problem as related to the Oil thinning as the motor heats it up. This almost always sets a CEL light. Have you seen the engine light come on?
I would give the IPR sensor a look at least. Make sure the plug looks good (no bare wires) and that the "tin nut" that holds it together is in place and hasn't vibrated off.
Another Free test is to unplug the ICP sensor. When the computer doesn't see a value from the ICP it will set a default value for the IPR to run on.
Other than that, I'm afraid the next thing you need is to get it on a good, professional, scanner to monitor things when you have this problem so you know what's not doing what it's supposed to (forget a cheap scanner like the Auto Parts Stores use, they don't work on our trucks).