Use ffmbc and DNxHD
You could try ffmbc, which is an FFmpeg version that adds support for common video broadcasting formats, including features like reading and writing Avid DNxHD videos. This is one of the most widely used visually lossless intermediate codecs and its file sizes are relatively small compared to raw video data, yet retaining very good quality.
You can also install the DNxHD quicktime codecs to add support for DNxHD to video editing applications and converters (e.g. Adobe Media Converter).
That way your clients could use the above tools to convert their footage to DNxHD and you can read it the same way. The file sizes are acceptable for internet transmission.
Can't test whether ffmbc also has support for ProRes. It says they don't have support for ProRes HQ.
If that doesn't fit your needs, you don't have that many options. The best possible video quality in relation to file size is achieved by encoding to h.264, probably using a decent encoder like x264. You will get much smaller file sizes, however the quality is not near perfect when you are talking about real studio applications.
It could be a viable option though. Just remember to let the clients use intra-picture only encoding and a low Quantization Parameter (e.g. High Quality setting).