The search service is not able to connect to the machine that hosts the administration component. Verify that the administration component 'GUID′ in search application 'Search Service Application' is in a good state and try again.

Question

Another post with a well-known title. Believe me, I know. Here's my setup;
- 1 Server 2012 WFE, SharePoint Server 2013, totally up-to-date, including the september 2014 hotfix
- 1 Server 2012 DB, SQL Server 2012
Installed SP 2013 using PowerShell, with the AutoSPinstaller. Worked like a charm. Got everything up and running, with some tweaking here and there to customize it to fit my situation. Now, I can't get the Search Service Application to work. Must have created,
deleted and recreated it at least 30 times. Used both PowerShell scripts, PowerShell line-by-line, Central Admin, heck, I even went so far as to use the configuration wizzard... No luck. I keep on getting the message that search cannot connect to the machine
that hosts the 'administration component'.
In order to avoid answers that suggest all the things I've already tried, here's a summary of the various scenarios I followed:
Tried both a dedicated application pool as well as the SharePoint Web Services Default
Timer job job-application-server-admin-service is running and not showing errors
IIS 8.0 is installed, so is .NET 4.5 (not the known perp of IIS 7.5 and .NET 4.0)
the get-SPEnterpriseSearchServiceInstance -local returns a healthy, online state
the SPEnterpriseSearchQueryAndSiteSettingsServiceInstance is also running
FireWall is disabled; registry has the BackConnectionHostNames modified with the necessary FQDNs
Accounts used to install and / or run the serviceapp all have sufficient rights - tried a dedicated managed account, SP_2013_SearchSvc, the SP admin account, and even the original Farm account; all to no avail, I keep on getting the error message.
Even tried stsadm to start the server search running - NOTHING WORKS!!!
As you might understand, this is driving me nuts. About to miss my second deadline, and no amount of IISresetting is making this go away. Been stuck on this issue for far too long, now (my searching is measured in days and weeks instead of hours, by now).
Whoever helps me solve this - you will have my eternal gratitude, and a nice bottle of Prosecco. Or whatever's your poison. You need to come get it, though. I´m situated in the Netherlands. Hey, you always meant to visit Amsterdam and see for yourself, right?
Thanks, community, for coming to my rescue!

Answer 1

Thanks again - Alas, I've been there. Deleted Search a dozen times, at least, and tried installing it, initially using a PowerShell script (tried several scripts actually, from full-blown total Search Applications with extensive topologies to the most basic
of basics 'please just start without showing me errors'), PowerShell line-by-line to see where things went South, next tried installing through Central Admin (hoping that it was my own stupidity in overlooking things and hoping The System would get it right
for me), and eventually even tried using the config wizzard as a total and utter last resort - Nothing worked.
At first, I found out that removing a Service App needs a *little* bit more work than simply removing it through Central Admin, but by now I can truthfully state that if there's one thing I've become supergood at, it's removing Search Service Applications.Totally.
I will check out the article, though - I realized early on in my SharePoint experience that regardless of what you think you know, there's so much more to find out. I know, that's almost philosophical. That is, my friends, indeed the point I've reached...