Thanks Julie. I replied with comments in the same thread on Stack Exchange. For quick reference for other readers, my response is below:
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Thanks Julie - I appreciate it. I tried a couple of different things based on your post. First, I removed the fixed cost entry for the task in question, and instead created a cost resource (with a per unit rate of $80,000). I assigned the cost resource to the task with an estimated usage of 1 unit, then re-baselined that task (with roll-up to summary tasks.) When I did this, for some reason, the Planned Value (BCWS) would not pick up the $80,000 cost, even when I set the status date well beyond the time for which I entered the actual usage. Neither did the Earned Value (BCWP). However, the ACWP did pick up the $80,000 cost. So it still left me with very large artificial variances. In the end, I simply decided to remove that element from the schedule entirely, since it has no potential to deviate from the planned value, and I am more concerned, at this time, with tracking the progress of the actual work effort.

In addition, upon further reflection, I decided that the magnitude of the $80,000 cost was so large in proportion to the relatively small weekly labor costs of $3K-$4K that a positive schedule variance for that task (if completed ahead of schedule) would severely obscure any negative variances in the labor tasks when the project was viewed as a whole. (At least until the original planned date of the $80,000 task had passed.) This was an additional reason I chose to drop it.

This results in an overall cost picture that is not entirely accurate since it doesn't include the $80,000, but it allows me to more effectively track the work being done on the project. And in case anyone is wondering, this technique is being used on a small project as a "work out the kinks" exercise before being applied to larger efforts. That is why I am spending so much monitoring effort on a set of tasks that is relatively small.