Ultimate Addons for VC Composer — 1 minute delay

I’m working on a website that uses several fairly heavy plugins. The speed is reasonable for normal viewing, but it’s impossibly slow on all the admin pages.

I’ve noticed that every admin page takes just over a minute to load (except those that take a multiple of ‘just over a minute’). This shows up as ‘TTFB … 1.1m’ in the browser’s inspector, or like this with curl (with cookies deleted):

* Connected to www.johnmeriton.co.uk (185.119.173.239) port 80 (#0)
> GET /wp-admin/nav-menus.php HTTP/1.1
> Host: www.johnmeriton.co.uk
> User-Agent: curl/7.58.0
> Accept: */*
> 
  0     0    0     0    0     0      0      0 --:--:--  0:01:05 --:--:--     0< HTTP/1.1 200 OK
< Date: Mon, 02 Apr 2018 18:09:36 GMT
< Server: Apache
< X-Powered-By: PHP/5.3.28
< Pragma: no-cache
< Expires: Wed, 11 Jan 1984 05:00:00 GMT
< Cache-Control: no-cache, must-revalidate, max-age=0
< X-Frame-Options: SAMEORIGIN
< Referrer-Policy: same-origin
< Connection: close
< Transfer-Encoding: chunked
< Content-Type: text/html; charset=UTF-8
< 
{ [788 bytes data]
100  326k    0  326k    0     0   4942      0 --:--:--  0:01:07 --:--:-- 75519
* Closing connection 0

The problem goes away if I deactivate the “Ultimate Addons for VC Composer” plugin, but doing that breaks various bits of the site.

Has anyone else seen this sort of problem?

This is with WordPress 4.9.4 running “The7.2” theme in 768MB of RAM.

Plugins:

• bbPress 2.5.14
• bbPress Login Register Links On Forum Topic Pages 2.2.5
• Contact Form 7 5.0.1
• Go – Responsive Pricing & Compare Tables 2.4.5
• Juicer 1.8
• Music Store 5.0.16
• Page-Links Plus 2.4
• Revolution Slider 4.6.3
• Soundcloud is Gold 2.5
• The Events Calendar 4.6.3
• Ultimate Addons for Visual Composer 3.5.3
• WPBakery Visual Composer 4.3.4

The page I need help with: [log in to see the link]