If I was looking at building a custom rifle right now, I would take a hard look at the Insite Arms actions (I would also highly recommend them to build your custom - they are the only gunsmith in Canada that I would trust with my money).
Other solid options are the Defiance action and Surgeon. The Defiance feels great, I run it on my match rifle. If you do get a Defiance, I recommend getting the bolt turned down if you plan on shooting in dusty/dirty conditions. Defiance's are built to tight tolerances, and can cause issues in the field. I had to clean my action out twice a day while shooting the Shoot for the Green PRS match in Oklahoma this year. Other Defiance shooters had the same issue, however Surgeon shooters had no issues. If you are just shooting on a square range, then the tolerances of the standard Defiance will suit you fine.
I hear good things about the bighorn actions, but have never handled one so I can't say much about it. The Ultimatum action has an incredibly heavy bolt lift, so I definitely wouldn't recommend them. BAT's feel really nice, really tight tolerances, but again not great for field use. Stillers feel cheap and gritty, but I guess that's why they are on the cheaper end of the spectrum for actions.
Give the guys at Insite Arms a call, they will get you sorted out. They have a lot of experience with different actions, and shoot competitively as well.