The 4k videos from Sony a7iii are quite large by default, suggestions on HQ ways to compress?
Well first, the a7iii at 100mbps is far from lossless or even minimally lossless. It's highly compressed in a 4:2:0 or 4:2:2 colorspace depending on your recording selection. The files are incredibly compressed when compared to what's considered minimally lossless or lossless compression algorithms. Shooting 4K at a "near" lossless level would require 4:4:4 and a codec such as REDCode at a compression of 4:1 or 3:1. These files are astronomically larger. 

As far as in camera, you're limited to what the camera provides as options, in terms of 50mbps, 100mbps, and so on. 

Your only real option to compress down and reduce file size would be to run the files through an encoder, either a real time "live" encoder which captures the video from the camera's HDMI out, or in post production, using Adobe Media Encoder or a similar application. 

With 4K, you could compress down, if you are happy with the color and don't plan to do any additional color correction later, to a 4:2:0 H.264 or H.265 codec using an MP4 wrapper. Using a Variable Bitrate, depending on your content/how much motion/detail/etc, you could likely get very good results with bitrates in the 25-50mbps VBR, allowing a Max Bitrate to be set up to 100mbps. 

Adobe Media Encoder is available from Adobe and comes with Adobe Premiere. Your best bet if this is something you need, is to run some trials, and to find the best "acceptable" bitrate you can live with for archival purposes.