Such constructions are a matter of style, so there is no single "correct" way of dealing with them.
If I refer to The Chicago Manual of Style (17th ed.), 6.95:
Parentheses—stronger than a comma and similar to the dash—are used to set off material from the surrounding text. Like dashes but unlike commas, parentheses can set off text that has no grammatical relationship to the rest of the sentence.
Although I'm somewhat familiar with what you're doing with the parentheses in your examples, I believe that Chicago, at least, would not recommend putting text inside of parentheses that actually does have some kind of grammatical relationship with the rest of a sentence—especially if doing so causes awkwardness.
In general, you should write sentences in such a way that if the parenthetical information were removed, the surrounding text would be completely unaffected. (In other words, the grammar used outside the parentheses should be completely unaffected by the text inside the parentheses.)
As for slashes, here is Chicago, 6.106:
A slash most commonly signifies alternatives. In certain contexts it is a convenient (if somewhat informal) shorthand for or. It is also used for alternative spellings or names. Where one or more of the terms separated by slashes is an open compound, a space before and after the slash can make the text more legible.
he/she
his/her
and/or
Hercules/Heracles
Margaret/Meg/Maggie
World War I / First World War
Although it doesn't specifically mention its stance on grammar around slashes, I suspect Chicago would say that, as they are just shorthand for longer (and more formal) constructions, if their use causes a problem, then use a longer construction instead.
In other words, when such constructions become grammatically awkward, I suspect the "proper" thing to do is to rephrase rather than to look for a specific rule of grammar (which likely doesn't exist).
For example:
Extreme votes on a Stack Exchange post often indicated that there was an agreement or disagreement.
When you see spam on Stack Exchange, you should case an upvote or flag.
They ship traveled across a sea or ocean.
On the other hand, if you are using a style guide that does say what to do in such circumstances, then follow its advice.
