Yeh, String choice was gonna be my next thought and if any of them were better to go with than others because of tuning issues (Dont think it would be an issue but Im sure there are some poor choices to avoid out there LOL). For years Ive used the Ernie Ball Slinkys but have gone to the Elixirs, and have bounced around to many other brands throughout.
I just pulled out my Sarricola that has been in the case for a long time (Years). Forget what strings are on it. It has a Floyd Rose Trem and Line Lock on it. It was still dialed in and I couldnt get it to go out of tune. I think the line locks and Floyd really help at keeping it once set-up.
As for the string choices, I believe a good string choice and set-up is needed for any Hard Tails or acoustics to help keep it in tune, (along with set-up, things like good tuners, the graphite dust on the nut and environmental controls). This is the area I need to watch/work on