This is a fantastic question! Unfortunately this was missed in connectapi, but I just created an issue to track it! Once this issue is closed, this should be easier to accomplish!
Unfortunately, my time has been such lately that I have not had much time to dig into connectapi development, but am hopeful that will change soon 
In the meantime, unfortunately the set_schedule_* function helpers do not have the ability to do this. However, you can use the lower level set_schedule() function (which allows arbitrary arguments).
You would want to make a request like this (see the set_schedule_* helpers like set_schedule_minute() for hints to get started)
client <- connect()
my_content <- content_item(client, "my-guid")
my_variant <- get_variant_default(my_content)
my_schedule <- get_variant_schedule(my_variant)
# akin to set_schedule_day()
set_schedule(
my_schedule,
type = "day",
schedule = list(N = 1),
start_time = Sys.time(),
activate = TRUE,
email = FALSE,
timezone = "Universal"
)
Specifically, you want to add a timezone = "Universal" or timezone = "America/New_York" argument, where "Universal" is the name of a timezone in the list. You can get the list of possible timezones adhoc with:
client <- connect()
client$GET("timezones")