It looks like 8arrows and I were typing at the same time with similar advice!
I only have a quick minute to reply but thought I would to just give you some ideas to ponder right away as you need them. With my boys once we began implementing a schedule, I looked at the times on the schedule as a general rule of thumb rather than legalistic times. So, for instance if something on the schedule is meant to take 15 min., as long as the child is working I allow a bit more time if needed (like 5-15 extra min.). Once I can see we are stretching beyond that and are headed toward getting far enough behind that we soon can't recover, I jump in and help the child recover if at all possible. To do this, I might do all of an English lesson orally, assigning none to be done on paper. Or, I may write out the math problems from the textbook to help the child move more quickly. I might downsize a math assignment a bit if needed. Or, I might put away or set out a child's materials open to needed pages to move him along. I may write a younger child's answers to DITHR, while he dictates them to me to save time. Or, I might sit right by a child pointing out text or redirecting while he works to keep him on task. I might read directions aloud from an older child's guide while he follows them, or I might send the kiddos for a much needed break while I quickly check their work to see why they might have fallen behind. Anyway, these are just a few ideas of how you can partner with your kiddos to keep them on track and happily moving through their day.

So, these are all things to consider.
Next, I'll share that I have a "finish school" time in the afternoon for my third son who is currently in RTR. This is a 45 min. block of time that is a part of his schedule (after his lunch, recess, and work in the warehouse break) where he returns to his schoolwork and finishes anything he did not finish earlier during the school day. This works well for him right now, as he has learned he prefers to get it done then rather than have it left in the evening. However, when we were training him in diligent work habits when he was younger, we had a work time in the evening after supper when he worked with his Dad on anything he had not finished during the school day with me. This worked well for me, as it needed to be dad who enforced the finishing rather than me!
In your son's case, when he begins melting down over the handwriting, I would jump in to stem the tide right away by saying something like... "Alright, I can see that you are overwhelmed with the amount of copy work today, and you will have to work up to doing all of it eventually; but to help you get started today, since it is a longer passage, I will write the first sentence (or two) to get you started. Then, you need to dry your eyes and get going with the rest. Let's see how much you can get done then in 10 min. if you work hard the whole time." Often, once kiddos see the length reducing before they begin, they feel more able to do it. This is true of any assignment they find overwhelming!
Then, head away to do something else after setting the 10 min. timer. Be sure he knows he doesn't have to finish in that amount of time, but just needs to work diligently. If you return and he has shown progress, he can either finish (if he's close to done) or set it aside to do the rest later. If he has chosen not to progress in the 10 min., simply let him know this means he'll have to finish later and set the work aside to be done at the later time you've designated for leftover work (either in the evening with dad or in the late afternoon).
If he does not work hard during the leftover work time, then you award the consequence at that time. This means you are giving the child every chance to succeed without drawing battle lines all throughout the day. You'll only have one time that you award the consequence. You want your child to see you are partnering with them to get their work done instead of lying in wait to take away privileges (even though you really aren't, they see it that way)!
Also, if the child ends up with quite a pile of work to finish during the "leftover work" time, both you and your husband (and your child) will be able to see that the day wasn't very productive. You can discuss ways to do better the next day then.

But again, you are partnering with the child to help them be successful.
Anyway, these are just some thoughts you can ponder to see what might work in your own family.
Blessings,
Carie