I'm still confused with some of the complexities of how HBD handles service time. In a current scenario, I had a player accrue 10 days of Major League service time last season (he was injured in Spring Training as a AAA player, and only made it back for the last 9 games of the regular season). With these 10 days he's got, do I need to wait the required 20 days plus an extra 10 to ensure he gets that extra pre-arbitration year? Or can I just call him up after 20, since the remaining Major League days plus his extra 10 still falls short of 172?

I'm pretty sure the answer is, yes.  Arbitration eligibility is based on total number of days in the ML.

You can check this at the start of the season by moving your mouse over the ML Service number on the player page.  If he's got 0.10 days, then you'll need to keep him in the MinL 10 extra days.

You're considering having the player miss 1/5 of the season. If I was trying to make the playoffs, I'm not sure I'd swap that for saving some money years down the road. You might not have a playoff contenting team then. A lot happens in 3-6 seasons.