You are experiencing a paradoxical problem.
You understand the concepts, but you misapply them.
You barely finish tests in time, but you have had great confidence that
you did them perfectly or nearly perfectly.
Many people find they "freeze up" on tests due to stress,
and they then forget how to do things.
Possibly you have the opposite problem.
You may be too relaxed.
In my experience, to do well on a timed exam I need to be in an unusual
psychological state. I did not quite realize this until I had been
out in the workforce for a few years, where I had days, weeks, or even months
to work out the solutions to problems, and then decided to to back to school.
I found out I had forgotten how to take timed exams, and had to relearn it.
While out of school I had not forgotten how to do math,
but I had come to take twice as long to work a problem in an exam
setting than I did when I was a student.
A little panic (but not too much) can keep you moving and
help you maintain a focus on doing what you need to do to answer a question.
A little fear (but not too much) can make you more alert to mistakes that
you may be making.
Clearly, whatever you've done during practice has not helped,
except for a some minor improvements in your technique.
Actually, improvements in your technique should be a major goal of practice,
not an incidental byproduct.
Forty hours a week is an awful long time to spend on practice;
somehow, you need to practice much more effectively in less time.
I have rarely if ever tried doing the same problem multiple ways on an exam,
but I find it is useful to do the same problem multiple ways
outside of an exam setting.
There are various benefits to this. One benefit, of course,
is that you get practice in each technique you use,
but a particular benefit is that you have a chance to compare the
effectiveness of the different techniques that can be applied to a
particular kind of problem: which ones are easier to apply,
faster, and less error-prone.
The best technique for one kind of problem
may not be the best for another kind of problem, even when it is
applicable to both kinds of problems.
In fact, the best technique for someone else to solve a particular
problem may not be the best for you to use on that same problem;
this is something that only you can discover for yourself.
In short, the point of practice is to solve problems faster and with
fewer errors. If you see no improvement in speed and no improvement
in accuracy, you need to try different techniques or different variations
on your techniques.
The particular example you give, transforming $4(c+b)$ to $4c + b$,
is an all-to-likely mistake to make.
We write formulas out in a sequential fashion, left to right,
but the distributive law does not work in such a sequential fashion:
it's more like filling in the cells of a rectangular grid.
If you are multiplying a multinomial of $m$ terms by a multinomial of $n$ terms,
you are (in effect) filling in the cells of an $m \times n$ grid.
Every cell needs to be filled with the product of some term from
the first multinomial with some term from the second multinomial.
Distributing a monomial (such as $4$) over a multinomial (such as $c + b$)
is really no different; the grid in this case is merely $1 \times 2$ cells.
If you remember that every term of the product of your
input expressions needs to be the product of two terms from the
input expressions, I think you're a lot less likely to simply copy
the $b$ from one line to the next and forget to multiply by $4$.
There is even a technique in the U. S. Common Core math curricula that
has students literally drawing a grid in order to perform multiplication.
I have never done this myself, but I do find that a mental "grid" is
a useful visualization.
An easy and quick check of my accuracy is simply to count the number of
terms in the product: if I multiplied an $m$-term multinomial by an
$n$-term multinomial, there should be $mn$ terms in the product.
(For this reason, I will often delay combining terms, for example I may
write $+4xy$ and $+2xy$ in two places in my answer rather than just writing
$+6xy$ once, until after I've counted the terms.)
For a complicated product where there's a chance I did one term twice and
forgot another, I might methodically step through each term of the first
multinomial and (for each term of the other multinomial) check that I have
written the product of the two terms; and when I find that product I literally
make a mark to check it off so I don't count it again.
In some cases I have even written out products of multinomials in
"long multiplication" format (as if I were multiplying multiple-digit numbers)
on a piece of scrap paper.
Come to think of it, maybe that Common Core grid could be a useful
technique to use literally, sometimes.
You don't necessarily want to use any of the techniques exactly as I have
described them, but you do want to find techniques that work for you to multiply multinomials by other multinomials or by monomials.
You need to find techniques that are fast and accurate when you use them.
You also need to find fast and accurate techniques for doing every other
thing on which you have made errors in the past.
There is unlikely to be a single "silver bullet" that will fix everything.
The patterns to look for probably aren't going to be recurring throughout
all the mistakes you make; you might want to consider any mistake you have
made more than once to be a "pattern".
After you have found fast and accurate techniques to do a few of the
operations that have been giving you trouble, try the
techniques again and make sure they are still fast and accurate.
It does no good to discover a technique if you later forget how to do it.
Until you can take a past exam paper, or a set of exercises from a textbook
comparable to one of your exams, and completely work them out under exam
conditions with plenty of time to spare (checking this with a clock),
don't tell yourself you have mastered the techniques or even understood
And once you have mastered suitable techniques, and learned how to recognize
which techniques to apply to which problems, you should be finishing your
exams quickly enough that you do have time to apply some of the other
self-checking methods that have been suggested.