firstly, all three will suffice and will give you some sort of benefit albeit not always the best benefit for your job!

as a SCH you can play around with each of the three rings depending on what you want to spec towards for a fight vit, pie, det, as for me imo the allagan ring is not good on a SCH, the last thing we need is pie, our highest valued secondary stats are Crit and Det, never pie.

Hero's + allagan : 26 mind/ 20 pie/ 16 crit/ 8 det

Hero's + Ruda: 26 mind/ 8 pie/ 16 crit/ 11 det/ 11 SS

in this setup I have to say the ruda ring is the better, think of it this way you are losing a some pie (which you don't even need) and gaining a whole new stat in spell speed, also not big on a sch but any help to faster heals is a good thing! Plus you are adding more determination which also help our heals, while at the same time getting a moderate pie boost from your hero's ring alone. tbh there is no coil acc as of 2.1 that I feel is better for a SCH if its not myth or EX primal then go with crafted a prioritize the spec you want!

as a healer our priority is to have better heals! the hero's and ruda combo would be the ideal choice to "have better heals"