Good Project Advice

Kevin,
You are absolutely right that it is a bit of a challenge to model in years. Here are some of my observations:
1) The reason 12 months is not accurate is because it uses 20 days per month as the default conversion factor (File, Options, Schedule). A more precise number would be 21.75 days per month ((365 – 52 * 2 weekend days) / 12 months) , but decimals are not allowed in this field.
2) The reason 52 weeks does not work for you is not clear to me because it does for me, 52 weeks goes exactly for an entire year (Jan 1 until Dec 29 with Dec 30 + 31 being weekend days. This is an exact hit as far as I am concerned in terms of scheduling.
3) The reason 365 days does not work is because the Duration field in Microsoft Project is in Business Days, whereas you entered 365 days that are calendar days, which creates a difference of about 104 weekend days (= 52 * 2); you should enter 356 – 104 = 261 days (business days), which yields a very good result as well: it is just one day off (task ends at the end of Jan 1st of the next year instead of at the end of Dec 31)
4) 365 edays is scheduled through the weekends and is a good model, but it assumes all weekend days are work days and that you work 24 * 7, so this not a good way to model Work (effort).
I propose you enter 52 weeks or 261 days from now on. I hope this helps.