I'm dropping in for something during SXSW during the week and looking to find good parking around the paramount and moody. I'm checking the SXSW site as well, but wanted to check here for any good ideas. I don't mind paying a premium.
Try SpotHero. I just checked the Friday of SXSW and you can reserve a spot for the day around 3rd and congress for $20. Ive used it twice - its pretty easy although each lot seems to have their own procedures and they could use some standardization...
here is a promo code for $5 off if you want (I get $5 too)