After renaming my files in chronological order, Lightroom is then grouping them by camera type

I have no idea why file naming should not be happening as you wish, but it is not necessary to make use of filenaming in any case when working in the Library or in the Develop module. You can sort by Capture Time and then the specifics of filenaming or of camera type, will be beside the point. If Lr considers one camera to be inherently producing 'later' or 'earlier' photos than the other, then that is a more fundamental issue of metadata interpretation.

Sometimes differences in how timezones / daylight saving corrections are treated, or varying camera settings such as "travel" vs "home" timezone, can lead to oddities. That variation would then be seen reflected in Lr's date/time metadata - not only in the renaming.

For example, even if both clocks have been set to report the same apparently sychronised hour, the photo timestamps from two differently set cameras may have differing real-world 'meanings'. I'd have thought when it is the same camera brand, and provided the cameras are set the same in all respects, results should be consistent - but some experiment may still be needed. Especially when travelling: different practical outcomes may be achieved by changing the clock time, vs by changing the stated timezone.