Skipjacks

Drive to work on Mondays with 4 extra suits/shirts/etc and leave them there (assuming you have some place to put them)

Ride the other 4 days.

It's a 2 mile commute so it's not like you're losing out on a ton of exercise for your 1 missed day.

You could also just leave your suit jackets at work (assuming you have a place to store them) all the time. It's not like you need to dry clean them after every use. Suit pants will be okay in your panniers for your 20 minute ride. A dress shirt might or might not be. You could leave dress shirts at work with the suit jackets, then just bring them home in the panniers at the end of the day. They can either be quickly ironed or cleaned at home so you don't need to worry about getting them wrinkled on the way home.

The pants will be fine though. I do it nearly every day. And I wear khakis, which are more wrinkle prone than your average suit material.

As for sweating, don't sweat it (haha I crack myself up). It's a 2 mile commute, not an endurance race. I live in Maryland so I have a similar climate as you and have a similar 2 mile commute with hills. I get 'slightly sweaty' on the hottest mornings at worst.

Remember that even on the hottest humid day in the mid atlantic, it's usually 75 at worst before 9 am. (I said USUALLY. On those insane July days during a heat wave that we get sometimes, just drive)

On my ride TO work I don't push it too hard. I give myself plenty of time and have a nice relaxing ride. I show up to work, towel off and change and I'm fine. On my ride home I push the bike hard and get a really good workout in, often making my 2 mile commute into a 10 mile meandering joy ride and I get hot and sweaty and gross....but when I get home there is a shower and change of clothes waiting for me. So who cares?


EDIT: I just realized you were from the SF Bay Area...okay so the humidity is going to kill you...for about 3-4 months. Then you'll get used to it and it won't be a big deal. When I was in the Marines I did a 3 month training in Southern California with the 72 degrees and 0% humidity. I felt like I could conquer the world in that climate after growing up on the East Coast. It was like I was hooked up to an oxygen machine 24/7. I had so much energy I had trouble sleeping! Then I got used to the dry climate...and I felt normal. Then I came back to the East Coast and I could barely breath for a couple months and felt like I was drowning just from walking around in the soup we call air. But I re-adjusted to the East Coast moisture soon enough and all is well now.

So if you're just coming East and aren't used to the humidity yet, it's gonna suck. But once your body adjusts the sweating on a 2 mile leisurely morning commute when its' 75 out really won't be that bad. The ride home when it's 95 and 80% humid will was a wet disgusting mess no matter how long you live here.