How to block auto-downloading files, or whitelist website and let me choose exactly what to block?

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Background

I need to check on some website from time to time (here). The website is quite simple, showing a time that some file was recently updated, and allows to download it.

I use an addon to monitor it, available for both Firefox and Chrome:

• https://chromewebstore.google.com/detail/distill-web-monitor/inlikjemeeknofckkjolnjbpehgadgge
• https://addons.mozilla.org/en-US/firefox/addon/distill-web-monitor-ff/

The problem

Thing is, this website has some issues with any ad-blocking addon together with this monitoring addon:

1. The website detects the ad-blocking, and blocks the normal behavior of it, reaching this website.
2. If the ad-blocking addon is disabled for this website, each time I reach it, either via the monitoring addon or manually, it auto-downloads the file. I don't want it because I want to download the file manually only when it's newer than what I already have.
3. Blocking Javascript alone also doesn't help, because then the webpage doesn't work properly, not reaching the state of showing the file information and button to download it.

What I've tried

1. I tried to white-list the website, and then finding how to block just the part that causes the auto-downloading. I can't find how to do it. In fact I can't even find how to do it for simple things, such as elements of the webpage, like when I choose to add more things to block...

2. I also tried to find how to block the auto-downloading, but I can't find anything similar. In addition, I tried to find an addon that does just that: auto-blocking downloads of a file from a specific URL. Still nothing...

3. On both Chrome and Firefox, there is a general setting for confirmation of downloading, but this isn't something I want for all websites. Just here, and even here I just want it to be blocked until I manually press to download the file.

4. I tried to contact the website owner and the website-monitoring addon owner. Sadly didn't help.

The questions

1. Is it possible to tell the ad-blocking addon: "Don't block anything on this website except exactly what I'm manually enabling about it" ? If so, how, and how can I tell it to block just the part related to auto-downloading

2. Is it possible to add a rule of "block auto-download of files on this specific URL" ? If so, is it possible to make it also work when excluding the website from being blocked?