I am not aware of an OSM based map for Garmin devices that is made for trucks, in other words, probably tags like maxheight are simply ignored. You can create your own map using mkgmap and that would allow to ignore those roads so that an alternative route is calculated.
If you have an OSM based map from Garmin you should ask Garmin for support.
In my experience OsmAnd will respect max height (if it is turned on in the routing options), however it could be an unit issue. I’ve only ever seen it work in metric units, so for starters I would convert to meters and see if it starts working then.
I know he made some maxheight edits in the UK, so he would be the person who would know if feet and inches values in maxheight are readily useable. (Personal gripe maxheight:imperial is a bad tagname as the largest country to have feet/inches values is the US which left the British Empire before the (British) Imperial standards of weights and measures.)