You probably already know and have done everything I'm about to say. Our site is not that large, on shared hosting, and has been, not consistently, but frequently, VERY SLOW (60 seconds!) to load pages and especially to make any kind of edits on the control panel. So I just did the following in our cPanel:
Changed from PHP 5.5 to 7.0
Increased max_execution_time from 60 to 90
Increased mem_limit from 128M to 256M
Increased upload_max_filesize from 2M to 8M
Increased post_max_size from 8M to 16M.
I know little about this, but it is zippy now! Pages are loading before Firefox can even make a full circle in either direction.
UPDATE: OK, some not-too-scientific stats:
PHP 7.0, mem_limit 256M
HomePage initial GETs(on F5 refresh): 870ms 1.03s 1.11s 938ms
CP SaveAndContinueEditing inital POSTs: 10.47s 3.92s 3.18s 2.37s 3.57s 4.54s
PHP 5.5, mem_limit 256M
HomePage initial GETs(on F5 refresh): 1.23s 1.08s 1.28s 1.42s
CP SaveAndContinueEditing initial POSTs: 8.52s 4.06s 4.1s 5.15s 5.08s 3.63s
PHP 5.5, mem_limit 128M
HomePage initial GETs(on F5 refresh): 1.04s 1.44s 1.14s 1.25s
CP SaveAndContinueEditing initial POSTs: 4.15s 5.21s 4.33s 6.41s 4.31s 3.9s
I am not able to duplicate the incredibly slow responses I had previously, in which I frequently could walk away from the computer and come back and it hadn't loaded yet. When I said zippy, I meant a second or two instead of 30 seconds.