Thanks for the input, guys.
Qaanol, why would say that your examples are any better than with "and"? I think you may have misunderstood my question: your examples do not contain any partially-parenthetical compound subjects. There are already established rules for handling OR (and AND) in non-parenthetical contexts like the ones you listed. To wit
The conjunction or does not conjoin (as and does): when nor or or is used the subject closer to the verb determines the number of the verb. Whether the subject comes before or after the verb doesn't matter; the proximity determines the number.
If we return to the question I originally asked, I don't see why "or" would be any clearer "and". There are just as many situations where "and" feels unnatural as there are for "or"--which is to say, two situations each.
"He (or she) is..."; with or without the parenthetical, it will be singular. No problem.
"He (and she) is.."; it would be singular alone, but with the parenthetical it would be plural. Weird
"She (or they) is..."; would be singular alone; but with the parenthetical, our closest subject is plural, so we should expect a plural verb. Weird
"She (and they) is..."; would be singular alone, but plural with parenthetical. Weird
"They (or she) are"; would be plural alone, but singular with parenthetical. Weird
"They (and she) are"; plural with or without the parenthetical. No problem.
"They (or the others) are"; plural with or without. No problem.
"They (and the others) are;" plural with or without, no problem.