Thought I would A-vs-B Zoho Desk with Zendesk, and I gave up on Zoho after fifteen minutes

I need a chat support widget with one agent. Zendesk will do this for $5 a month (not bad!) but Zoho has a free tier for up to three agents, so I figured I'd give Zoho a shot.

I put the Zendesk widget on one web page and it works out of the box. Perfectly.

I put the Zoho Desk widget on a second page and this is what I encountered:

The chat widget icon shows up off-screen, and there's just a box that says "Leave a message We're offline" — but the blue icon is off the screen. Just a sliver of the left side of it appears. (Screenshot attached.)
The "Leave a message We're offline" box is skewed, and cut off.
If I open the box and try to click inside it, the whole page stops interacting with the mouse. Even the elements that are not part of the widget. Even if I close the widget I can no longer click on links on the website or highlight text. It breaks the web page.
When I open the widgetI can type in the fields, and I can tab back and forth between the fields to enter name and email. But if I try to click on "Enter your name" or anything, it breaks the web page again. The mouse stops interacting with the entire page (even elements that are not part of the widget).
So I figure I'll try submitting a message just tabbing. No dice, though! There's no way to tab to "Submit," and if I click on "Submit" it (again) breaks the web page.
Tried it on mobile and it doesn't break the web page! However it's larger than the mobile screen, and I can't access the "Submit" button. It won't scroll, so nothing can happen.

Some important info about this:

My website is a static HTML page, just HTML and CSS. No php and no javascript (except for the Zoho widget). It's the simplest possible website you could try to add a widget to.
I am using a MacBook. I tried this in Chrome, Safari and Opera. Same behavior in all three.
Using an iPhone SE (first generation) I tried this in Safari, Chrome and Firefox. Same behavior in all three.

I'd bet dollars to donuts that the issue is with my CSS stylesheet interfering with elements in the widget. Which really seems sloppy. But I don't care enough to suss out what the issue is.

I could fuss with Zoho tech support and wrestle with it to try and make it work, but Zendesk worked out of the box in every configuration — and is just physically more attractive to boot. Seriously, what the hell is with the chat box saying "Leave a message We're offline"? That is not easy on the eyes.

Not to mention I see over and over again in these community posts that Zoho tech support is slow and less than satisfactory. So that's not a battle I'm willing to wage

I'm still using Zoho Invoice (which I've used since 2015) because it's a good free invoicing management system for the volume I do (very small side business, a few invoices every couple months). But I thought I'd leave some feedback here so Zoho knows why this customer is willing to spend $5/mo elsewhere rather than mess with their product.

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