Typing in large markdown buffers is slow due to corfu and flyspell. How to address?

When I type in a large (1000+ lines, tens of thousands of words) Markdown buffer, the typing feels slow. My profiler reports this

Memory

Bytes % Function

14,151,043 33% + flyspell-post-command-hook
11,394,237 27% + corfu--post-command
8,081,767 19% + command-execute
8,069,640 19% + redisplay_internal (C function)

CPU

Samples % Function

1032 27% + flyspell-post-command-hook
740 19% + corfu--post-command
676 17% + redisplay_internal (C function)
653 17% + ...

My config for Flyspell and Corfu is

;; Corfu
(use-package corfu
  :custom
  (corfu-auto t)
  (corfu-auto-prefix 1)
  (corfu-auto-delay 0.1)
  :init
  (global-corfu-mode)
  (corfu-history-mode))

;;Flyspell
(add-hook 'flyspell-mode-hook
      (lambda ()
        (setq flyspell-issue-message-flag nil)
        (flyspell-buffer)))

How can I address this bottleneck? I've tried narrowing the buffer, but it seems to change nothing.