How to pinpoint why a specific ressource (image or library) slowing down page load

So, without actually getting on your network(s) and diagnosing in detail with you, an answer here will likely be more of a "point you in a direction" and see if it works.

That said, I take a sort of Occam's razor approach when dealing with this kind of thing.

You stated:

"the web based interface faces no slowing down when accessed from outside the office. that is, it slows down only when used behind our local network."

This here, if truly accurate, is the piece to key in on.

The issue SHOULD lie then somewhere within that "local network". It's NOT on the externally hosted server/application, otherwise the same issues could be replicated from another location.

So where? You've already swapped out a few pieces of network gear to no avail it would seem.

Here's what I would suggest you do, which may sound simple, but work from the farthest external point of your network backwards:

1. Take a laptop that has NEVER been on the local LAN, isn't part of a domain, etc. and attach it directly to the local network's ISP. Directly is the key. Put a laptop directly on the ISP's network without a firewall or similar in the mix and see what kind of responses/performance you then get and compare it to your known good external setup that works fine.
2. If you don't see issues in step #1, proceed to move the laptop one layer back, directly attached to the ASA firewall, and then test again through the firewall.
3. If no issues at #2, then go back another layer, this time behind the managed switch.
4. If no issues at #3, then you know it isn't a network issue.

And so on and so forth (trying a client that has "issues" externally, etc.) until you at least can objectively say what/where the issue occurs, even if you don't know why or specifically what is causing it at a particular "layer". Then you start a deeper dive into that specific "layer" if you will.

You will probably need to use nmap ( or wireshark for example ) to inspect the local network, it can help you find a windows computer having a virus and sending thousands of spam arp requests, or a user using a bittorrent client or whatever can saturate your local network or your internet upload

The other option is that most ISPs are far from perfect . . . perhaps sometimes the ISP have some packet loss or upload stability problems. Installing a monitoring tool like smokeping, and monitoring a target on the internet could help you see this ( packet loss , slow upload, slow ping ), and also allow you to see when that happens ( everytime john doe is at the office and plugs his computer to the network ? ).