The most likely explanation is that the Runcloud setup was serving from cache and the Enhance setup was not. The load spiked to 80-90 because the CPU was maxed and the system probably ran into swap. This didn't happen on Runcloud because more requests were being served from static cache and not PHP.
An intermittent 503 error usually means you're hitting the PHP worker limit*. With Apache/php-fpm this is configurable in the UI. With LSPHP (OpenLiteSpeed/LiteSpeed) this is currently set to 50 and is not configurable - this limit will be configurable in the very near future however raising the limit is unlikely to help if the load was already 80-90. The real solution is caching.
Enhance is primarily a tool for selling mass hosting and creating managed hosting products, it is not a managed hosting product in itself. As such the default settings are very conservative and no caching is enabled by default. However I think you can easily get comparable performance to Runcloud with a few small changes.
If the site doesn't have the LSCache WordPress plugin installed, try installing it. You can check it's working with the LS cache tool. The "out of the box" defaults, when combined with LiteSpeed or OpenLiteSpeed should resolve the issue for you. If it doesn't, I would be happy to have a look - just send a support ticket with the relevant info.
AdamM The problem is that even when the client disables the cache or disables the plugin, it exposes the server to overloading. I talked to Adam about it. This is supposed to be fixed in v2 litespeed.
This is a behaviour which can be configured but it's not a bug that needs to be "fixed" as such. For mass hosting, default/forced caching is often undesirable. Default cache settings will be a configurable in LiteSpeed v2.