Wow, I feel for you. I'm re-working my rig right now, and it's true, things that should be straightforward (order something, it shows up, get on with it) frequently don't work out that way... which, when you're on a deadline, is a real pain.
e.g. I recently ordered a Neumann KMS105, a week before a jazz gig I especially wanted it for. How much simpler could it get? Was assured the mic would be with my local dealer Wed (gig Fri). Pay special courier charge to make sure of it. Ring on Wed to check it's in... told it hasn't made it, but would definitely be there in their delivery on Thursday (and they'll refund the courier charge). Ring Thursday... told that they're sorry, but the reason it hasn't shown up is that their "head office" never actually ordered it from the distributor! Deepest apologies. And no, there's no way they can get Sennheiser UK to deliver it to me in time for soundcheck the next day. How helpful.
I ring every dealer I can think of that keeps any stock of Neumanns. Nothing. (although they'll all order me one).
So I have to spend four hours that evening, when I should be preparing for the gig, rushing 20 miles across to the opposite side of London, to the only rental company that has any, before they close for the night. (I'm not a regular customer of theirs, so no, they won't deliver, and they need a copy of my passport etc...). I have to have a 105, because I put it in the spec, and the artist is expecting a Neumann for the female vocals. It costs me £30 to rent.
Then on my way home, I drop in at a central London dealer (it's 8pm now) to pick up another bit of kit I've ordered, and guess what? They've got a brand new KMS105 in stock, in my preferred nickel finish. At the same price as the dealer I ordered with. But of course, I already have the rented one in my bag.
And the final kicker? You'll love this. I discover when I arrive at the gig the next day that the female guest vocalist can't make it!
Grab four hours sleep after getting in from the show, then get up and spend another two hours racing across town to get to the rental co before they shut (early on a Saturday). All so I can return a rented mic that I didn't use.
No matter how well-prepared you are, stuff can happen that's simply beyond your control. I've learned to expect it now, you can kind of smell it coming.. which is when I try to have some vague backup plan, just in case.
I know, this doesn't help you much right now. All I'm saying is, I feel your pain! Doesn't matter how clearly you explain things, how accurate your drawings, how thorough and unambiguous a specification document you hand them, some half-wit can always screw it up for you
But you still have to do all that stuff, if only to prove who's screw up it is. Thankfully it sounds like you've avoided that particular argument. Good work. Bet you're glad you did those drawings.
Sorry, yet again, a longer post than I meant!
Paul