Show "partial" results (e.g. plots) once available instead of all at once (full page load)?

Question

I am trying to build a Shiny app, that shows n different plots on one page and releases them (shows them) one by one as they become available/computed instead of all at once (full page load).

The plots have a dependency on the same input-variable (e.g. Number of bins) but have different data sources (live database queries). I want the plots to become visible as they are ready/computed one by one, so the user can start to work with the data/plots as soon as possible while other plots are still loading. In reality my app has like 10 or more plots/tables that need to calculate, so the time adds up.

As all plots have the same input dependency (Number of bins) the change of the input invalidates all elements on the page (they turn grey). To retrieve data (db calls) and render the plots each of the plots might consume n-seconds to be computed (example: 3 seconds). At the moment the user will need to wait until all plots are computed (3 + 3 = 6 seconds) to see both plots at the same time. My expectation of a "lazy" load would be that the results would show up asynchronous as long as there is no dependency to each other.

My questions based on below example are:

1. Is there a way to show plot 1 after 3 seconds, and show plot 2 after another 3 seconds?
2. I would like to make use of the Shiny withProgress() function, to show updates on the status of each plot. Would that still work?
3. What if plot 2 depends on plot 1 calculation (output/variable)?

Example (I modified the Shiny boilerplate code for this example):

library(shiny)

ui <- fluidPage(
    sliderInput("bins",
                "Number of bins:",
                min = 1,
                max = 50,
                value = 30),
    plotOutput("distPlot1"),
    plotOutput("distPlot2")
)

server <- function(input, output) {
    output$distPlot1 <- renderPlot({
        Sys.sleep(3) # Simulating a slow database call
        x    <- faithful[, 2] # Actual data for the sake of this example
        bins <- seq(min(x), max(x), length.out = input$bins + 1)
        hist(x, breaks = bins, col = 'darkgray', border = 'white')
    })
    output$distPlot2 <- renderPlot({
        Sys.sleep(3) # Simulating a slow database call
        x    <- iris[, 2] # Actual data for the sake of this example
        bins <- seq(min(x), max(x), length.out = input$bins + 1)
        hist(x, breaks = bins, col = 'darkgray', border = 'white')
   })
}

shinyApp(ui=ui,server=server)