Note that all the following are speculations as I am not 100% sure how the systems are set up.

Currently, my Inventory and the two town pages take minutes to load each. The pages used to load as quickly as the other aspects of the site previously, which I found strange to have them start acting up lately.

After some thought I found[?] that, for the town pages, it's the Town Barracks that are causing the major slowdown. I have many stables and tabs for my pets, and since the page is trying to load everything at once [possibly for smoother user interaction with the town pages] my army of pets are causing the page to lag trying to load them all to display in the dropdowns.
As for the suggestion, based on my above hypothesis, visiting the page should load the first stable only. Then selecting another stable the user has will make the page load that stable's pets. Just so that all the pets a user has aren't attempted to load in one go.

My main issue with slow inventory loads is trying to open my many mission satchels. Each time I open one, the page refreshes upon closing the reward window, so I have to wait another minute or two to open the next. I would like to suggest having it so that the page does not refresh upon opening satchels, like how putting items into the Broker works. The reward window closes, but I can go right ahead to put another item in the Broker without the wait.

Thank you for your time.

@Draco,

Yep. :\

The infrastructure of the Site was originally built with all users having only 1 stable and a maximum of 200 pets. Since now that number has drastically increased for some of you, it's way too much information trying to load on some pages.

I am currently working on the Party Manager page which will also do the similar task of loading all of your stables and pets, however I'm going to code it to load each Stable on demand. Once I get that figured out and coded, I'll implement it into all of the other places on the Site that load your pets.

And that should solve all of the issues you talked about.