見るようにします : try to see 間に合うようにします : try to make it on time
My understanding is that ようにする can be used also in cases where a prolonged, concerted undertaking may be involved. From questions I've asked friends, I might use it in cases where I might choose to say "endeavor to..." rather than when I might use "give it a try", where 「てみる」is more suitable. I don't think it's limited to that, but perhaps it sounds a bit "heavier" than just 「てみる」 which can sounds "light". For the 「てみる」 case, you might stop trying after trying just once.
does this differ in meaning from Vte +miru?
I agree, Miki-san
#3881, #3886 Japanese is not natural. My suggestions are #3881 あなたは、英語で自分の言うことを理解してもらえますか。 #3886 私は、私の言うことを人に理解してもらえなかった。 When I was a student, I took a test to translate "make oneself understood" into Japanese. If you answer like 自分自身を理解されるようにすることができる, you surely get "X" as the Japanese is not natural, even you can get the meaning.
#3888 ある in the end of sentence is funny. You should delete this as you have #3889,
I believe this way to say "try to do something" also means that the action is necessary or should be done.
する and します are both "to do". so するようにします means "do-kind of-will do" ?? seems odd...
...as opposed to 'verb + you ni suru/kokorogakeru etc.' = to try, to decide
dbx's examples are mostly "clause + you ni", indicating a purpose.
Formed from 'verb + you ni suru' V = verb
It looks like these examples from the DBX are for a different usage of this construct...