@ Jerry
First time I’ve heard that Connections was poorly written … I usually hear quite the opposite from other devs who use it for their clients with site as large dbs, more than 20K entries.
Any way … I know it is not your hosts job to debug the code, but, if they have specific area(s) which they can point to as being an issue being caused by Connections. I will definitely look into those and make what ever fixes may be necessary.
With that said, I browsed around your site and I see what you mean by slow loading. Some definitely seems “hokey”. I’ll try to explain.
When I click a state and I’m presented with a list of city links. These seem to be hand created on the page, yes? Ok…
Lets say I click on Idaho and then click on any city, looking at the network activity, the first thing that happens is a 301 page redirect. This redirect seems to be the bulk of the page load. You can view this for yourself by opening the pages in Chrome with the dev tools open, hit F12 and then click the network tab. After the pages load scroll to the top of the requests. Every page I visited the first request is a 301 redirect. That important because a redirect in WP will occur before the Connections shortcode runs and that’s the meat of any processing Connections does. Anything before that, Connections related, takes mere milliseconds.
When I visit PA, thing are better. It seems most pages/cities do not have this redirect and the page load in about 3–5 seconds which is about average for a WP site without caching (I see W3TC is being used, but lets ignore that for the moment) even and WP tuned managed hosts. This load time is indistinguishable from page load time where Connections is not being used like the About us, Bail Jumpers, Bail Tails, FAQ and Feedback pages.
It could be that the current service level that you are subscribed to with the host is not enough. It appears the site might be hosted with GoDaddy. Is that correct? At the very least, the domain seems to be registered thru them. Any way, if you are on their basic shared hosting plan you could very well be being throttled (very common on shared hosting, cycle have to be available to all the accounts on the server which can range into the hundreds) depending how popular your site is. That could explain why page load times vary quite bit, even why some pages and the admin fail to load.
Back to W3TC. I see after a page is cached by W3TC, the page loads in about a half second. You could setup its preload or prime the cache. What this does is it’ll crawl your site in the background pre-caching the pages. That could help significantly as you users should only hit a “slow” page if it isn’t already preloaded in the cache. Even though I have not used it yet (I will be giving it a try very soon), I’ve heard some pretty good things about WP Rocket (I’m in no way affiliated), ie lighter and faster than W3TC while being easier to configure. There is a cost attached to the plugin but it could be worthwhile checking out if you have the time and funds available.