Well, my saying goes "Anyone has exactly as much power over you as YOU grant them".
When you give way to the bully, what you really expect? Think twice.
My experience is that bosses like you describe have their position because of people who chose to obey. Then if the project go south it's blamed on the executor. While if nobody notices or chooses to show the tremendous waste, and the project still manages to vomplete they shine as benefactors.
That all would not happen without volunteer serfs.
If I don't agree with something i speak up. If one wants to prescribe me HOW to do what is really my job and my responsibility, I just say "you do it". Yourself. In your name.
Those who think it's a good way to get you fired are probably right -- but if it actually happens I'd consider it a huge gain. In practice it never happened to me, the boss just backed off realizing the no power situation. And being skilled survivalist rather covered up. (Especially as dong the suboptimal way or even escalating it would likely got him fired or seriously injured.)
Part of your job description (I guess, it sure is of mine) is to keep doing the right thing. Using the most economic way. Ok, make it one economic way. And prevent making huge detours or tracing backwards.
It's established industry wisdom that we're supposed to use sharp tools. That one is quite easy to defend. And if one comes up with gratuitous restrictions, he can be drown by applying the five whys.
On the other hand there may be some team-related factors to consider. But that thread leads far.
Suggestion? That would require many details over the board. But if you happen to work in a "large" company that has legal department you can make a good use of it. Especially if you have position "ombudsman", I suggest to consult right away. They are really helpful, and that part can be done in full secret till you learn all your options and decide what to chase. If you're honestly are after doing your job correctly and act in the best interest of the company, even going against bosses, you're entitled to a deal of protection.