I’m sorry that my two suggested solutions didn’t suit you, even though these suggestions have a significant impact on the page effect of the guest mode on your site.
Using your suggestion with the CSS would almost completely negate the benefits of guest mode. The guest mode is designed in such a way that the first time a page is loaded, maximum optimization is carried out, regardless of your setting, in order to achieve the fastest possible loading time. Everything that is not absolutely necessary is excluded from the store. But all the prerequisites have to be right for this, so that ideally you only see a blank page that flickers for a very short time. The loading of external sources, above all Google, Facebook, etc., impairs the requirements considerably, making it difficult to find a solution for this page effect. If you haven’t already done so, please change the following settings:
CSS Combine: On
UCSS Inline: On
Load CSS Asynchronously: Off
Regardless of your issue, the cache plugin seems to be misconfigured to a significant extent, e.g. the cache for non-logged-in users on the homepage is private. As a result, the first request on the home page is too slow for each user. The actual advantage of the guest mode is thereby destroyed. This has the same consequence as if the guest mode were deactivated. As a result, the unsightly page effect also occurs much more significantly.
I therefore advise you to set all settings to default and then use the presets. You are on the safe side with the presets, because the individual settings of each preset are coordinated.
As for guest mode, you might want to read that:
https://blog.litespeedtech.com/2021/06/01/guest-mode-for-wordpress-in-lscwp-v4-0/