Have an Alienware and never had any problems, game runs perfectly 
My brother though, he ran the game on a veery old pc, I don't even know the specs but it's at least 5 years old, he had to play with everything on low and every loading took like 10 minutes.. plus the pc would sometimes just shut down cause too overheated (even though he had a fan placed just right next to it to cool it) and wouldn't turn back on without waiting a while.
I honestly don't know how he managed to finish the game. Must have been stressing..
10 min loading screens.. Just.. wow, that's some serious dedication to gaming on PC.
My husband's computer (Alienware) has had nothing but problems since he bought it. The video drivers crash hard every time he tries to run a DVD. For a while, it would overheat constantly, but it turned out that whoever assembled it at the plant left the plastic cover on the processor before attaching the heat sink. That's right. There was a layer of plastic between the processor and the heat sink. It was melted in place. Now that we've got that problem fixed, it no longer overheats every 5 minutes, but we haven't attempted to run DAI on it. The machine has enough problems.
I've got a home-built system that runs the game fine on the highest settings. Every once in a while, I'll get an inexplicable DX crash, but it seems to be a random thing. I'll go for weeks without a single one and then I'll get three in a row.
That is like the dumbest thing I have heard of for a professional computer company to do. I am sorry that the person who built that PC is alive.
I had the same experience. I built my first last year (for Inquisition).
+1, same as meee!
Well I bought a new computer before DAI came out but in preparation for it. It's specs were 16GB RAM, i5 4670k CPU, and a GTX 760. I thought a GTX 760 would be more than enough, boy was I wrong. I can't play games on any setting lower than Ultra and having to play on Medium-High settings just killed the experience for me. I think I got to Skyhold before I realized I couldn't continue like this.
I've been waiting for this game since I finished DA2 and not playing it perfectly was a major turn off, so I replaced the GPU with a GTX 970. I finished the game with this card and it was an okay experience, I remember always going into the graphics menu since I still got stutters and wondered what to turn down.The 970 was almost perfect, it could run it on Ultra but with no MSAA. I can't play without AA so on one of my other playthroughs when I got to the Templar quest it kept lagging in that area. Even with MSAA off, I felt like I had an epiphany at that moment. I needed to buy another 970 to SLI for the first time and that's what I did.
The game is now perfect, everything on Ultra, with 4xMSAA. I have never looked back now. I finally have my dream computer and it is the best feeling ever! 
Have to ask what resolution you are playing at. I think my brother plays on high settings with a 970, which I convinced him to buy because he had a crappy old 550 Ti. I also actually bought DAI for him and after he played it a bit, he turned around and bought the game for his best friend, lol! I can tell you a 980 can completely own this game with maxed settings @1080p. That said, you've done well to future proof yourself by going SLI with the 970s. Wondering if you are overclocking those bad boys at all.
This goes in the opposite direction from the OP, but two years ago I thought about building my own rig for DAI. I've built several over the years, but decided that I didn't want to spend the time, and I wanted to have an end-to-end warranty.
Spent six months spec'ing out various configurations on a couple of custom builder sites.
Went with a Digital Storm Slade.
Final Build:
i7-4770
16GB @ 2133MHz
GTX-770
1TB SSD
Other fancy stuff and 4-year hardware warranty
Cost (delivered):
US$2000
Couldn't be happier.
Pricing the identical components using Newegg it seems I paid about a 20% premium.
Totally worth it to have someone else do the work and stand behind it! 
(If you want to drool, check their Aventum 3 )
This is what I wanted to bring up. Building your own PC is by far the cheaper option.
Digital storm is prolly the best place you will find high end PCs at a reasonable cost.
Take this build for example (customized build to match one more similar to my own):
ASUS MAXIMUS VIII EXTREME (Intel Z170 Chipset)
Intel Core i7 6700K 4.0GHz (4 cores 8 threads)
16 GB DDR4 Memory @2666 MHz
1200W Corsair AX1200i
Blu-Ray & DVD Writer/Reader
1x SSD (1TB Samsung 850 PRO)
2x Storage (2TB Western Digital - Black Edition)
2X GTX 980 SLI
H20: HydroLux LITE: Integrated Cooling System (CPU Only)
This will cost you $4,618.
I picked something that was similar to what I have:
ASUS Rampage V Extreme
Intel Core i7 5820K @4.5 GHz (6 cores 12 threads)
16 GB DDR4 Memory @2400Hz
FSP Aurum PT Series 1200W PSU (+ Platinum)
Blu-Ray & DVD Writer/Reader
2X SSD (512GB Samsung 840 Pro)
2X Storage (2TB Seagate Barracuda)
2X 980 ASUS STRIX
EKWB Water cooling equipment (for CPU only)
This will cost you $3,543.96.
Looking at the prices, I saved about $1,000 just by assembling it myself.
Out of interest, what is the wattage of your PSU?
I've been toying with the idea of a similar setup. Currently have a 1000W power supply and a single gets 980 with the same processor as you.
You will not need a new PSU. The TDP on the 980 is 250W. If you have a CPU that takes even 200W and everything else that takes up another 50W, you will have room to spare.
How many watts do those Titans draw? I have an MSI 980Ti Lightning and it draws 450W. I was thinking of getting a second one, but I don't think 1000W PSU is enough to cover two of them and everything else in my rig.
How do you know your 980 Ti draws 450W?? I'd wager its prolly at least 100W below that. You should be fine with a 1000 W PSU unless you are Overclocking the crap out of it and even then, you prolly don't need a new one.