Carbonate them naturally upright. Chill them in your fridge. Attach the tap with the bottle upright (obviously), lay it on its side, then insert C02 cartridges, keeping it on its side. Stick it back in the fridge and keep it cold and on its side from then on.
I'm attempting to naturally carbonate with the full amount of priming sugar this time. I'll report back with my experiences. The worst thing about TAD is the way the carbonation changes over time as the CO2 cartidges add forced carbonation, but the extra head space causes the carbonation to change again, and as the CO2 runs out it changes, etc etc. It's very difficult to have a consistent pour from it. I'm hoping a full natural carb will change that.
I'm also using the full amount of sugar on my batch. This batch was in primary for 18/19 days and then crashed cooled for 24hrs before moving to a bottling bucket. I figured a lot of yeast probably settled out and I'd need the full sugar load. They've been in my basement at 69F nine days now and the bottles are firm, but no bombs.