Long Distance (~30mi) Bag Use
Unfortunately, you're probably not going to find a backpack that converts to a pannier in that price range. And most of them kind of suck for all day use anyway, even the high end ones. You can feel the hooks digging into your back so it's not comfortable for much more than carrying it from the bike rack to the office. 

Your best option is probably to use a rear rack and a basket. Then you could simply put your backpack into the basket for your commute. You can get a cheap bike rack for about $25 and a basket for about the same price. That particular rack is rated for 55 lbs and while the baskets don't list a weight spec, the Q&amp;A section below says that people easily load 25+ lbs per basket.

There are lots of other companies that manufacture similar racks and baskets, so it would be a good idea to shop around. Those were just the first ones that I stumbled across. 

You could also use a front basket as someone else suggested, but those tend to mount up high which affects your steering. And not in a good way.