So, it's worth asking around at your place of work to make sure there aren't shower facilities anywhere. Often a maintenance area may have one available or there could just be a shower somewhere that's almost forgotten because most people don't need one. Whether it's convenient or not for you if it does exist is a different question, but it's more possible than you might think that there's one around.

Alternatively, any chance there's a gym nearby and you need/want a membership? That could address the shower issue as well. Either way, I get wanting or needing to shower because even when my commute was just around five miles I tend to get sweaty enough to need it. Now that it's eight it has to be pretty cool and I have to have my layers pretty dialed in to not need to and still be comfortable riding in.