Katrina,
A couple of things jumped out at me in your post that I thought I'd respond to in the hopes you will be encouraged. First of all, I noticed that your son is in the opening two-three weeks of a new guide. This means that the amount of writing has gone up, along with much of the guide being new. Together this does have a learning curve that can take some time to conquer.
I'll share that for ALL three of older my sons, I noticed that as the written volume increased their legibility decreased. This is truly because of the reason your son already shared... with more to write and less time to do it within, something has to give and neatness is the thing that goes with boys.

Also, it is more tiring to push hard on the paper, so it isn't uncommon for kiddos to conserve their strength by writing more lightly when they know they will be writing alot! And, when you are writing alot, then anything else having to be done on paper (especially things with a blank page staring back at you like in the drawing lessons) feels like just one more thing for an already weary hand.
Couple this with the fact that your son is 12 and for boys that is when puberty begins setting in (as we have seen with all three of our oldest sons - and we are going through it now with our current 12 year old), and you have an emotional roller coaster on your hands.
So, here are a few tips that we have found to help our boys through this stage (which goes on for about 3 years unfortunately). But, it does wane in the third year.
First, be less critical about the penmanship. I know this flies directly in the face of what Charlotte Mason would say, as she would expect less done better, but there is a time where work that is assigned just must get done. This is that time. So, I would back off on the "making everything excessively neat goal" and remember that this is a boy with volatile emotions with whom you are working.

I have to remind myself of this daily with my own 12 year old boy!
Second, I would encourage him to trace as needed for drawing assignments. If he's drawing the solar system, use coins to trace around to make those perfect circles. Anytime there is a potential to trace around something or use a ruler for a sketching page, utilize that tool. This will save him much angst.

We've allowed tracing around bottoms of glasses, plates, buttons, etc. to make circles for our kiddos sometimes too!
Third, switch to using pencil on the pages if you are using pen. It will be lighter writing on the page, but as long as my boys can read it back to me, I allow light writing.

It is easier to erase and redo for a child who desires a clean copy and for whom frustration rises when things are spelled incorrectly or written incorrectly. Pen, on the other hand flows more easily on the page but it is harder to fix when there is an error. Ticonderoga pencils help here as they are stronger.
Fourth, I do have my kiddos read their work to me, and allow them to correct any mishaps as they read their work aloud. This is a quick fix and a quick way to correct errors without riddling their page with my marks. At this stage in their life, my marks seem to upset them. So, let them make their own changes with you by their side guiding.

If they can't read it, they correct it.
Fifth, if he'd rather type sometimes allow that... as long as it doesn't lengthen his day or the assignment. Sometimes typing is a benefit and other times it is quicker just to write something.
Sixth, now that you know that drawing and lab type assignments where he draws are a stumbling block, when those assignments come up take a few moments to talk about where things go on the page and make a couple light pencil guide marks our outlines to get him started. Once he can see a plan, he'll go forward more confidently. Knowing a child's areas of weakness and being there before intense frustration sets in helps so much.
Anyway, hopefully these ideas will help. We have our own 12 year old who also struggles with light writing, messy penmanship, difficulty with the blank page, a tougher time with spelling than my other boys, and a quick rise to frustration level right now too. He is a lefty who had to be a righty, due to an accident with his fingers on his left hand when he was young. These are the things we are doing to help him, and the mood has improved. Plus, he is still gaining, even if it isn't always pretty!

As I look back over how far he has come, I stand continually amazed! I just try to remind myself to compare my boys to where they used to be rather than to each other, as they are each so different.
I have also noticed with my older sons that the writing does improve again in later high school as they start to care more about being legible. So, remember you have years of ahead of you with which to tackle these concerns. My motto is to try to pick your battles during this stage!
Blessings,
Carrie