No need to apologize. First, "Given that information, would an H265 export still be recommended, despite there being a 1080p deliverable?" H265 should give a better compression and is more efficient than H264 and will be able to encode more high resolution than H264 without extrem file size and some better handeling for streaming purpose. But I don't think this is the main issue or helper here. You work on a 1080p sequence with 4k files only if you attempt to reframe some videos, like for an interview for example. But if your client finaly wants a 4k export...you'll need to reframe everything, loosing of course, the ability to resize your interview. So this is very important to know what will be the final export resolution before even start the production. If you're not sure, use two 4k cameras with different focals so you can edit in 4k all the way.Now if needed you can export a 1080 video from the 4k timeline. You can give a try to the " Use maximum Render Quality" in the Render settings panel and see if your render is any better with or without. It uses an other scaling algorithm than standard upscaling or downscaling algorithm if I remember well. Try and see. This being said, you have a 4k monitor meaning that if you look a 1080p video especially in full screen, it won't be as crisp as a 4k file since the pixels will be upscaled. After a brief look at your two examples on youtube on my 1920x1080 monitors, there is almost no differences. "One thing that did help was checking an option in the program monitor called "High-Quality Playback," which seemed to give me a little bit more confidence in the image ". High quality playback is meant for two main things ( as far as I know ). By default, when you use text and launch playback, the text will be a little bit pixelated to preserve computing, the same for some FX you may add on your videos. If you enable " High quality playback", the text and FX will play at full quality. Put a text on your timeline and have a try with and without. I don't know if it's clearer now, but hope it helps.
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