I had a similar issue with my Mark V. I forget where I read this, but it usually does the trick: amp on standby, watts set at highest setting, cycle through all of the channels on the footswitch. Flip the standby switch, and voila! no more pops.
I've enjoyed my Carvin 2x12 cab, and they have a 1x12 as well as a 2x12 vertical that has the footprint of a 1x12. Your Mark V will hang off of either side, but I'm guessing you already knew that it would be too big for any 1x12.
http://www.carvinguitars.com/products/112V...