I'm aware that (at least today's) English allows the use of a plural pronoun to avoid mentioning a gender of the subject. Example: _"Everybody can do what they want to" instead of "Everybody can do what he wants to." A typical use seems to be whenever the speaker does not know the sex of the actors and thus does not want to state it wrong or to let the phrase apply to both sexes alike.
As this example clearly shows, the numerus of the predicate then matches the numerus of the subject: "he wants" vs. "they want". This leads me to a dilemma if there are several predicates, associated to both the "everybody" and the neutral pronoun: "Everybody pays for what they get."
The first verb feels better to be in singular case ("pays"), the latter obviously must be in plural case ("get"), yet both refer to the same entity which can hardly be singular and plural.
To use plural case for both verbs ("Everybody pay for what they get") sounds strange in the beginning of the sentence, and the mixed numerus given before sounds a little as if it isn't reflexively meant, i. e. as if everybody has to pay for whatever some other group of individuals ("they") get.
What is the typical solution to my problem?
EDIT: To make this clear: I'm not asking about the singular they and its use, I'm asking about the "pay" vs. "pays" in my example (i. e. the verb of the "everybody") and about the observed or felt dichotomy of using a plural verb and a singular verb for the same actor in one sentence. Is there a more detailed answer to that besides "'they' can refer to a singular object and is to be used in plural form"?