Shaggy rug Pet-friendly alternative to a shaggy rug for room acoustics?

Positive reinforcement is a good training method.

Food and a Clicker produce great results with communication.

The dog can be taught to recognise the 'Click' as the prompt to Wee on the Shagpile (especially when the carpet cleaning service has just left the home). 

Each successful 'Click' that successfully produces a Wee on the Rug, will be positively reinforced by giving the dog a 8oz fillet of Steak. This really works!! Take note.

As a forewarning, the method can result in Turd being discovered on the Shagpile, or in a unfortunate bare footed discovery trod into the Shagpile. 

@triskadecaphobic I can second the recommendation for rugpadusa.com . Great variety of options; high quality and really good customer service.

The Superior Lock 1/4” works well for us under a few Nepalese hand-knotted wool rugs; I suspect they would work well under the washable rugs that @tcutter listed and the combined effect should give you good acoustic results.

If I got a carpet I would lay down and then roll up each listening session... will that would last less then a week before it was permanent. 

Indian Cotton rug(s), buy then wash to soften, best there is in my opinion

I’d use a thick 100% cotton blanket that is easy to launder.

Maybe a waffle/thermal style.

Fold it up when not in use.

DeKay