Trouble controlling axis location in R plotly subplot if multiple axes are used

I'm having trouble controlling the location of axis labels and tick marks for a plotly scatter plot created with R

I read similar issues on setting layout(margin = list(pad = x)) and modifying layout(xaxis = list(domain = c(x, x2)) but the behavior is not consistent between plot and subplot, even if the subplot is simply a duplication of a plt.

The below example is illustrative of the real scenario I'm working with. I have a multi-row subplot in which the user can select up to 4 traces. The below example shows an attempt with three. You can see that the two traces anchored to "left" overlap.

• Adjusting the pad argument to margin can separate the titles, but leaves the axis ticks and labels superimposed.
• setting layout(yaxis(anchor = "free", position = .03)) or some other similar code causes all elements in the subplot to disappear.

I couldn't find any working examples in my search that showed a scenario with a subplot and more than 2 axes per subplot.

I'm looking for help in

1. Fixing the below example.
2. Better understanding of how to control the axis placement in plotly subplots.

REPREX

plt1 <- plot_ly() %>%
  add_trace(
    data = mtcars,
    x = ~mpg,
    y = ~hp,
    name = "hp",
    yaxis = "y"
  ) %>%
  add_trace(
    data = mtcars,
    x = ~mpg,
    y = ~wt,
    name = "wt",
    yaxis = "y2"
  ) %>%
  add_trace(
    data = mtcars,
    x = ~mpg,
    y = ~drat,
    name = "drat",
    yaxis = "y3"
  ) %>%
  layout(
    showlegend = FALSE,
    yaxis = list(
      automargin = TRUE,
      side = "left",
      title = "hp"
    ),
    yaxis2 = list(
      side = "right",
      overlaying = "y",
      title = "wt"
    ),
    yaxis3 = list(
      side = "left",
      overlaying = "y",
      title = "drat"
    )
)

plt2 <- plot_ly() %>%
  add_trace(
    data = mtcars,
    x = ~mpg,
    y = ~hp,
    name = "hp",
    yaxis = "y"
  ) %>%
  add_trace(
    data = mtcars,
    x = ~mpg,
    y = ~wt,
    name = "wt",
    yaxis = "y2"
  ) %>%
  add_trace(
    data = mtcars,
    x = ~mpg,
    y = ~drat,
    name = "drat",
    yaxis = "y3"
  ) %>%
  layout(
    showlegend = FALSE,
    yaxis = list(
      side = "left",
      title = "hp"
    ),
    yaxis2 = list(
      side = "right",
      overlaying = "y2",
      title = "wt"
    ),
    yaxis3 = list(
      side = "left",
      overlaying = "y2",
      title = "drat"
    ))

subplot(plt1, plt2, shareX = TRUE, titleY = TRUE, nrows = 2)