7/16" ID will be really loose on 3/8" barbs, no way would I try that, I doubt you would ever get that clamped well enough that it wont leak.
If you have to neck down to 3/8" for that one block I'd just use 1/2x3/4" tubing on the whole thing. Then just get a foot or so of 3/8x1/2" tubing. Cut a little piece of it long enough to go over the 3/8" barb, then just slide you 1/2" ID tubing on over that and clamp it, that gives you a real good leak proof union without having to use reducers.
Or just use some reducers...1/2" barb to 3/8" barb Hose Adapter
If you have to neck down to 3/8" for that one block I'd just use 1/2x3/4" tubing on the whole thing. Then just get a foot or so of 3/8x1/2" tubing. Cut a little piece of it long enough to go over the 3/8" barb, then just slide you 1/2" ID tubing on over that and clamp it, that gives you a real good leak proof union without having to use reducers.
Or just use some reducers...1/2" barb to 3/8" barb Hose Adapter