As a father of three and a car enthusiast I love the topic of this thread!
I don't have the time at the moment to read through all six pages at the moment but wanted to chime in regardless. Apologies if these thoughts have already been mentioned.
Stay the hell away from vans unless it's a VW Syncro. 99.9% of vans are so f'ing ugly and pathetic. It's a billboard that you have just given up on life. And to the comment on this about insecurities - lol.
Any third row choice is a major pain in the ass if you don't have captain seats in the middle row. Only a couple of modern SUVs offer that - off the top of my head Tahoe/Yukon/Suburban and some XC90s (don't believe you can get RDesign with captains in the middle row.) The issue is there is no ease of access to a third row with fixed car seats whether forward or rear facing.
Three across is going to have more to do with the carseats than the actual car. One manufacturer that pushes three across ability, is super high quality/safe and looks decent is Clek. I luck out here as I have quite a spread between kid #1 and 2,3 and don't have to worry about three across.
In terms of actual options that comes down to personal preference. But take a serious look at car seat options that fit your needs before giving up to #vanlife
Carseats are expensive but relative to a whole new vehicle, you may be able to spend $1,500 on three new ideal car seats and end of story.