Your problem is that the [Date (filename friendly)] field is a calculated field, and is not user editable. So you can't directly update it using the "Fill Properties From Filename" function.
You need to update the [Date] field, which will then update the [Date (filename friendly)] automatically. That means you need to take the value from your filename in the form "20080302-135931" and convert it to a form that will import correctly into the [Date] field, in the format "2/03/2008 1:59 pm". Basically, you need to do the reverse of "FormatDate(Filename)", which converts the [Date] field to the [Date (filename friendly)] field.
Hmmm. That reverse conversion looked hard. So I created a copy of one of my image files, renamed it using the expression "FormatDate(Filename) - [Name]", and then deleted the [Date] field for that image, which then cleared the [Date (filename friendly)] field, giving me the same situation you are in. I tried a few expressions, and couldn't get it to work. Then I thought I would just try "Automatic" in the "Fill Properties From Filename" function, and boom, MC found the Date field and correctly formatted it. It only found the [Date] field, and not the [Name], but that is all you needed. I saved what the "Fill Properties From Filename" function was suggesting, and both the [Date] and [Date (filename friendly)] fields were filled in correctly.
Sometimes we just try too hard, for something that is simple. I still don't know how to do the same thing using a template, but that hardly matters!
The attached image shows my original image, my test image without a [Date] value, and what the "Fill Properties From Filename" function finds. Works a treat.
PS: Not good that Lightroom strips the time from the "Date Taken" field. That field should be sacrosanct and never altered.