I would def say to cover the rear ones. I have a 4.5ft BCI in same footprint cage and only have one small section of screen on the top with a CHE over it. Never had any problems with temps / humidity, etc. Also if you havn't done this yet, you should move the water bowl closer to the heat source.

Right now it's about 82 in the cool end and ~88 in the warm end. Most of the heat goes up and warms the two tubs above it.  It gets in the 90's in them. It rarely gets over 90 in either end. the room temp is usually between 73 and 78 depending on whether or not the door is shut. 

You might consider switching to a higher watt red or blue heat bulb and eliminate the CHE, they are notorious for drying the environment. Other than that, yes a big humidity box is a good idea. Do you have room for a rubbermaid tote? I'm thinking you could use one of the 56 Q shorts and cut a big hole on top and fill it with moss. Soaking is good but it needs to soak for at least 15-20 minutes to be beneficial.

CHEs dry out the air quite a bit. Raising humidity is pretty basic, reduce ventilation, increase surface area of water. For a cage that size, try a large cat litter box half full of water and see what that does. Water under the heat source is a commonly suggested method, but I always like to make sure there's another water source in the cool area in case your snake prefers the cooler water to drink. I have high humidity species so I use cypress and sphagnum along with large water containers and I spray a few times a week in the winter months. A humidity box is another good suggestion, put it mid-cage so its in neither the hot or cold area.

+1 on ditching the heat emitters and all the lights, switch to using a heat pad instead.  Vision cages do fantastic with the ZooMed brand heat pads stuck to the bottom of them; in the smaller models you can often get away with just the pad and no heat light at all. how are you only getting temps of 88 in there??  I've used a 60 watt plain old daylight blue bulb in that model before and depending on how close the basking surface is to the light, I can get surface temps well over 100.  <3 the visions for high humidity and temperature needy animals, they make a fantastic bubble of warm, wet air.

+1 for the sphagnum, pack a huge wad of it into a couple corners and keep it damp. Or, to keep your cage maintenance as simple as possible, pack it into a couple kitty litter pans. 

+1 on the heat pad.  If you put the water dish over part of the heat pad, this could definitely help increase humidity.  If you use a Zoo Med UTH, be sure to put that thing on a thermostat.  In my experience, the Zoo Med ones get really hot.  I like Ultratherms, but that's just my preference. 

I haven't read all these.

Humidity is water vapor and air pressure. You can have the CHE and a sealed tank and you'll get your humidity.

Your heat rising and vents positioned in the back like that draw air from the outside in, pull it through and spit it out the top. In normal room temp, if you sit a glass out, at 70 degrees it evaporates relatively quickly. You have to find your cages balance between airflow and moisture.

CHE's produce a very dry heat. I don't know why.

Close up your vents a bit. You'll see fog on the glass last longer the less airflow you have. But then this gets into health benefits of fresh air. This has been a great heated chondro debate.

I've found bowls of water are pretty useless in an open system. They don't evaporate quicker than the air flow. Therefore, humidity (since you lack pressure) drops.

Try a rolled up wet towel on one side of the cage, or a kitchen towel on the side (dunno how you'd get it there).

With arboreals, it's easy. The wet towel as a substrate provides an enormous amount of evaporation. With the damned ground dwelling fecal smearing terrestrials, it's a far bigger challenge. The rolled up towel though should provide good retention and surface area for adequate evaporation once you pressurize the system by closing the vents a bit.

Never share towels with other cages, if they get soiled throw them out. Cheap rags/dishtowels can be found at wally world.

we have a two columbian boas and in their cage we put pete moss on half and aspen on the other half, we keep the moss pretty moist. some people may disagree with this but we have had perfect sheds every time with out any health problems

Get rid of the lights and CHE's, hook up a UTH with a t'stat, and your troubles will be over!

(Beautiful boa btw, Peruvians are my favorite BCC!)

I have not read all the answers either, apologies for duplicating or contradicting....

I use microenvironments, basically moist hides.  The substrate within the hide is coco fiber or sphagmum moss, usually the latter.  Each cage gets two at least.  The cage substrate is newspaper.

I use this for any size snake.  My largest are my adult Indigo and WLP, but with a little creativity you could do it for a larger animal too.  The WLP and BRB also have large water bins to get into if they want.  I also add a moist hide to colubrid cages during shed.

Here is my typical moist hide, basically two very large plant saucers held together with plastic ties:

I use plastic containers of all sizes, holes cut on side to avoid moisture loss, they work great!  I love this one, it's for my WLP, it is a mixing tray from Home Depot filled with moist substrate, and an inverted plastic box with a hole over it, and the whole thing sits over a heat pad and under a RHP.  The WLP is in there a lot, sheds great.

So, advantages include (1) less total substrate, (2) easy clean up, (3) excellent moisture retention.  The disadvantage in my view is that they look like crap.  But I'm used to them and very happy with the results.  They work best for animals that don't like to defecate in their hides, like the Indigo and water python, but with the BRB and WLP I have to check for soiling regularly, because obviously this method also provides a great substrate for bacterial overgrowth.