Just got home last night and I figured I'd post a trip report.
Day 1: Slept in Boulder, woke up and drove to NCAR. We climbed Bear Peak and had great weather at the summit. We huffed and puffed a little but it wasn't too bad. Got back to the car just in time before some rain came through. Later that night we went to the Phish show. Not ideal to be on our feet for another three hours but the show was awesome!
Day 2: Drove west to Loveland Pass. We hiked up Sniktau, up the initial steep ascent to the false summit. It was more difficult but again, nothing to turn us back. We would have pushed for the summit but the skies started to look ominous so we turned back. Sure enough it hailed on us during our descent, and the lightning came not long after we made it to the car. We probably made it to something like 12,500 ft. by my estimate. We then drove through Leadville and ended up at Mt. Elbert's south trialhead (near Lakeview Campground). We slept in the car at the TH. My girlfriend had bad headaches throughout the night but we drank a ton of water, and she felt fine the next morning.
Day 3: Woke up around 5 am and decided to try driving up the 4WD trail towards the 2nd trailhead. We made it as far as the creek and didn't want to attempt crossing so we parked just before the creek on the side of the road. From there it was only a 1/2 mile walk to the parking lot and 2nd TH. We reached the summit around 11 am, no doubt winded from the altitude. It wasn't easy, and we both had headaches for the last 2 hours or so, but nothing horrible. Between the two of us, we drank 5 liters of water. Luckily we had no afternoon storms so were able to take our time on the summit and the descent.
So it is possible for flatlanders to get into the 14s on a short trip like this. I believe our success was due to hiking each day in increasing elevation (8,500 ft.; ~12,500 ft.; 14,440 ft) and relentlessly drinking water. It wasn't easy, but we were enough in shape and determined. Awesome trip in the end, thanks for all the advice!