As it stands, it seems that there is currently no way to obtain all the parts required to build the Garrison Auction House (it used to be in Ashran when it was active and now it’s no more).
Is there a way you can perhaps make those items available again in an upcoming patch perhaps?
Please and thank you for your time. 
Buy the mount.
The OP wasn’t asking for an alternative solution which costs literal millions gold.
Edit: not enough millions.
I am for convenience but I don’t see this as necessary.
But that’s the official response he will get from blizzard
Why would you even be in your garrison unless you’re leveling through wod content?
As far as I know, the Ashran parts are no longer required to build the auction NPC.
This is correct, they removed the Ashran parts over a year ago.
As others said: you no longer need the Ashran part.
Oh, I see. Thank you.
I thought they fixed that, so you could basically still buy it on the AH.
Ah, yeah they did; You just don’t need that part, as others said.
My Hunter bought the Garrison AH, on the AH, for 400 K in Legion 
Why would you do this? Because, you have a hearth port directly to the AH. So I found it worth it, for at least one of my characters to have that.
This character has 3 cloaks, with different cool downs, that port it to Stormwind. I still find it easier to do AH stuff with the Hunter, rather than having this one port/run down the tower/fly over to the AH; Ain’t nobody got time for that!
So they are no longer available to be farmed and you can only buy them for an exorbitant price off the black auction market? What am I missing here? o.O
Players can sell the individual parts on the regular auction house. I farmed most of the parts myself on an alt, then got tired of it and bought the last 2 parts I needed from the auction house. So you can still farm everything you need yourself, or you can buy them all on the auction house (if people on your server are selling them).
Maybe they want to work on WoD professions? Run old WoD dungeons? Old WoD raids? What does it matter, who cares the reason?
It might not be up on the AH when I need it. Or on certain low pop realms, it’s possible that it might not be up and no one is selling it or they are capitalizing on the rarity of it and that it’s no longer farm-able that they jack up the price exponentially.
I don’t know if you know this my friend, but WoD ended years ago. You don’t have to stay in your garrison anymore. You’re free!
Set your Hearthstone to a capital city and enjoy the fresh air 
All the parts you currently need are farmable–I did this just a few months ago. The Ashran bits that you can’t get anymore were taken out of the requirements. As to no one selling the parts you do need on the auction house, that’s quite possible–there’s not a lot of demand for them anymore.
The Ashran part is no longer required.
Ashran is still active - when that brawl comes up don’t those parts drop ? Actually you don’t even have to wait for the brawl - it is right under epic bg.
Oh nvm, I see they removed that from the requirement anyway.
I am frequently in my garrison, doing things like making cloth for bags, gathering ore and herbs for use in projects, doing the missions in case the experience item thingy mission turns up, doing the pet battles, etc. It still has its uses, and has the benefit of being no longer basically obligatory as it was in WoD.