Impracti-cowl?

Let me start this post off by saying this: I love the design of the finished cowl you are about to see and I do not at all blame the designer or the design for the tiny issues I have with my cowl. That said, I finished a gorgeous cowl and I'm not sure if it's practical for how I wanted to wear it, and therein lays my knitterly dilemma.

BMFA De-Vine, colorway Smokey Mountain Morn

This was the result of Star Athena's Mystery Cowl KAL, the pattern for which has since been named Sartorial Cowl. I think the pattern is a great match for this yarn, which grew a bit and relaxed nicely into the textured stitches after blocking. I still adore the yarn, its multiple plies gives it this great density and slickness. However, that density adds to part of my issue with the cowl: its heaviness and its length. There's really only one way to wear it:

And when worn this way, it's kind of like a 290 gram (10.2 oz) necklace. This sucker is HEAVY. This is mostly due to the bulky yarn, but the silvery metal buttons I bought for it don't help with the weight, either (although they matched so well). I have to sort of flop it over on itself like that in order for it to feel warm at all because it's far too large to be snug up to the neck:

And just a touch too short to be wrapped around twice:

I, quite frankly, don't know what to do! At this point, I'm really wishing I had  knit the small size, which would've been snugger around the neck but would've left me with a bunch of leftover yarn (mine was medium and large would've taken two skeins). I had wanted this cowl to be sort of an indoor cowl. My neck is always chilly at work and I wanted a little something to wear that wasn't really bulky and also wasn't a full-on scarf. I'm tempted to frog it and start over because the yarn is just too fantastic not to get worn, but it probably wouldn't get re-knit for months. I'm giving it a test drive at work today to see how it goes. What would you do?