The problem is worse when they have to send something back to me. I considered running a simple web app that allows you to upload a file if you know the secret URL like above but never got around to actually build it. Someone probably did though.
I have a local VM at home running a web server that can hold such files, but in AU decent uplink speeds are mostly a fantasy, so in the case OP described of needing to send to multiple people I'd upload it first to a VPS I keep that serves a similar purpose. This way I only flood my uplink once.
Obfuscated path for some very basic privacy, though of course you can encrypt and email password if that works better.
If it's going to happen semi-regularly, and the files are large and there are multiple recipients, then I'd look at BitTorrent. Most people have a client installed, or can install one fairly painlessly. Biggest challenge there would be that 6881 (etc) are often blocked, or at least monitored, on corporate firewalls.