Unless you have long arms, I bet life will be easier if you make that bed 3 feet wide instead of 4 feet. Most of the time, you won;t even have to walk around it!
I use concrete paving stones, stood on end, for walls. They make it easy to widen or lengthen a bed, like re-arranging lawn furniture.
12x12 x 1" or
8x16 x 3.4"
Just lean them in a little, and they're quite stable. Chink the angled corners with a broken piece, or pebbles, or let a little soil spill out. Or line the inside of the corner (below soil level) with a bit of heavy plastic cut from a soil-amendment bag. That keeps soil from spilling out, AND helps keep the corners from drying out first.
>> I'll have to either dig out the back or raise up the front to get it level.
Personally, I like a LITTLE slope to the base or floor of the bed. I have very imprevious clay, so I slope the floor to let water run off towards the downhill edge or corner. Just a few inches across the 3-4" width is probably plenty of slope for drainage.
To be sure I have drainage, I not only slope the floor, but also cut a few shallow trenches (just another inch or two deep) into the clay underlayer to help assure that the roots have air right down to the clay level.
If you have a very dry climate and want to water as seldom as possible, a little plastic under the bed and part way up the downhill wall will make a "bathtub" and hold water all too well - at the cost of drowning those roots! Maybe leave some gaps or holes in the plastic but still expect it to slow down the run-off.
P.S. I expect that, over several years, organics and roots and worms will pentrate even my hard clay, uner the good soil. The "florr" will gradually become pervious to water and roots. So I made sure that even if the clay softens to an extra depth of 6" or so, there will still be drainage from the bottom of that new soil.