A Heli-Coil is useful beacuse it would allow you to use the same size screw.
As far as "not being available in an inch," there is usually a minimum length in which they bother to make a certain diameter of screw. For instance, you can get 1/4"-20 screws with 1/2" underhead length, but you can't get 5/16"-18 screws easily in anything shorter than 3/4" Following that pattern, figure that 3/8"-16 screws will have a minimum underhead length of either 3/4" or 1", and 7/16"-14 screws would have a minimum length of 1" (unlikely, I think) or 1-1/4" (more likely,) but I'd have to check.
It's the same sort of standard that governs the threaded length of screws - if the shank is three "diameters" long or less, it's fully threaded. If the shank is more than three "diameters" long, they only thread three diameters' worth, unless you specially order full-thread screws. For instance, a 1/2" screw 1-1/2" long or less will be fully threaded, but 2" or longer will only be threaded for 1-1/2" of its length.
If you can get a 7/16" screw to work (probably with a stack of washers...) you'll end up needing to "clearance drill" the engine mount bracket - meaning that the hole will now need to be at least 25/64" or 15/32".
Simply stacking a batch of washers under the screw head would look a little shonky - but it's up to you. One or two can usually be hidden - six or so (which is what you'd probably need) gets ugly.
5-90