I don't know of any indoor ranges that will. Elm fork has a target free berm you can fire into, but no targets so you can't see patterning. The private range I belong to in Poolville (Parker County Sportsman Club) will let you (even have a metal pattern steel so you can spray paint it and then see you pattern). I, too, have a 930SPX and went through your exact process, with little luck.
Sent knowing my life is boring unless I'm looking down range. And that most of you are jerks.
Garland Public range has a clay pigeon range on one side and a short range by the pistol range on the other side for shooting still targets (like boxes).
Great Southwest Gun (indoor) in Grand Prairie allowed shotguns the last time I was there about six months ago. You'd probably need to call and ask about slugs. Their website lists handgun calibers up to .45 acp and rifle calibers up to 7.62 X 39. I don't see it on their site but they charge an extra $10 for shotguns. I'm guessing because the shot will destroy their target backing, and the extra mess. They only have 8 lanes at 20 yards but its nice and air-conditioned and the ventilation is great.
I took my CHL class at Great Southwest Gun in Grand Prairie in Feb. and asked them about bringing my shotgun in and they had no problem, they did tell me that they prefer I use slugs when I shoot it though.