How to install coat hooks securely when holes don't line up with studs (batten depth?, length of screws?)
I would think that if you used a nice hardwood for the wood strip that it can work well if it is 0.75 inch in thickness. Attach it to the studs with screws that are 2.5 inches long. Then use 0.75 inch screws to mount the hanger bracket to the hardwood board. Remember to drill proper type pilot holes for the screws rather than just trying to force the screws in without pre-drilled holes. It will be MUCH stronger if installed this way. 

The hardwood such as oak or birch is recommended because it will hold the screws much more firmly than a soft pine board can. Would a pine board be strong enough and hold the screws OK for this application? -- Probably.