Eureka!  It is the (rather thin) VGA cable. 

 

I noticed some variability in the issue, and earlier had wiggled connectors with little effect. However, flexing the middle of the VGA cable made the problem come and go like I was fiddling with rabbit ears on a TV!

 

Tested the 2007FP with the nice beefy VGA cable that came with my older ViewSonic VP181b and the problem was gone, both on another PC and on my laptop. 

 

I'm now using a 9 year old VGA cable from my junk box, and interestingly if I look closely and vary my viewing angle, I can still see the issue very faintly - but I really have to know what to look for, and it is not noticeable for normal use.

 

The VGA cable that came with the Dell is just over 6.5 mm in diameter; the ViewSonic one is 8mm.

 

I'll be contacting Dell about a new (& better) VGA cable.

 

Hope this helps others.

 

P.S. Why do virtually all of today's laptops not have DVI-D output?

A follow-up post in case someone at Dell wants to pursue a cost saving:

 

Apparently there is no separate SKU for a VGA cable, so there is no option other than to send me another monitor. I resisted - there has to be a way to just get a cable - but no, I was told, they need to send me a new monitor, and I return the old.

Good news: I was able to catch the rep and have the shipment changed to just that VGA cable. 

 

Thanks, Chris.