OK, I do see that the 500-frame limit is probably the problem or part of it.
There are other ways to try this that might work better.
The GIF is currently being exported using Save for Web. That’s usually OK, but Save for Web has some limitations related to it being very old code that needs updating. I think the 500-frame limit might be one of those limitations.
Option A: Lower the frame rate of the video timeline. Use the Set Timeline Frame Rate command in the Timeline panel menu. For example, if there‘s a 500-frame limit and you need the GIF to be 60 seconds long, then 500/60=8.333. So if 8 frames per second is acceptable to you, set the Timeline to 8 fps and it will need only 480 frames for 60 seconds, and it will work (I just tried it). If 8 fps is not smooth enough, use Option B…
Option B: Use a different GIF converter. First create your animation in any application you like that can do it (Premiere, After Effects, Photoshop, etc.). Then export that as a video file; .MOV or .MP4 formats are fine. Drag the video and drop it into in the free app Gifski, and convert the video to GIF using that. For conversion to animated GIF, Gifski has some serious advantages over anything from Adobe* that I am aware of: Gifski does an amazing job of preserving image and color quality given the very limited 256 colors available in GIF, has a range of options that make it easier to get the file size down, and, it doesn’t have a 500-frame limitation. I have definitely created animated GIFs over 1 minute long (over 600 frames long) using Gifski.
If there is still a problem with text clarity, try increasing the Quality setting in Gifski, but keep an eye on how much the final file size grows. In Photoshop, a way to affect text appearance for screen-based exports is to change the Anti-Aliasing setting for a text layer in the Character panel or in the Character section of the Properties panel.
(I was going to also suggest, in Photoshop, trying the command File > Save a Copy and choosing GIF because they recently upgraded that with more modern code, but I tested it and sadly it too is limited to 500 frames.)
*Although Adobe Media Encoder/Premiere doesn’t appear to have a frame number limit for animated GIF conversion, there isn’t much control over animated GIF settings; and it produces much larger file sizes, takes much longer to export, and often doesn’t look as good as an animated GIF by Gifski. You can also try the online animated GIF converter offered as part of Adobe Express, but I don’t find that one very useful because of the lack of control over the result. Another one you can try is the drag-and-drop Convert to GIF option in the Quick Actions panel in Adobe Bridge, but that only seems to use the Adobe Express online service with its very limited options.