Best used turntable/arm combo for under $7,500.00

At that price point, you have some great options and many folks (like I am about to do) will recommend the turntables that they eventually settled on.

Before I get to my turntable choice though, I will say that the Amadeus is a good one-stop solution. No need to worry yourself about arm upgrades. Though when you move into the price range you are discussing here, then the Amadeus' fit and finish are not going to be particularly competitive. With other tables you may be getting a more substantial table (steel or metal frames rather than MDF, a suspension rather than squash balls). But, that said, I used to own an Amadeus and it sounded GREAT.

What did I replace it with? Townshend Rock 7. You can read the TAS reviews of them to get an idea of how they compare sonically. Townshend Rock 7 also feels like a more bombproof build (steel frame, with suspension). And for better or worse you can think abotu upgrading the arm should you get the itch. I love my Moerch DP-6 arm with it. The the arm is a bit tweaky but I love the swappable armwands! I have also heard great things about the Helius Omega tonearm and have seen that it is often paired with the Rock at shows. That is the arm I am most interested in hearing with my Rock. Maybe one of these days.

All of that said, if at all possible I would look into auditioning the tables on most interest. No substitution for hearing the table yourself. We all respond to different aspects of music differently, and some tables may be better suited to reproducing certain aspects of music better than other aspects. This will then intersect with your preferences in terms of what you listen for most in music as well as the characteristics that are most present (and again, important to you) in the genres that you listen to.

You have a serious amount of world class tables out there. You can go for a Direct Drive Technics SP10 variant. You can go for a Lenco based Idler drive by Artisan, or indeed a Garrard 401/301. These are both fuss free combos. Yogiboy is right about the SME 10. I happen to have an Amazon Model one - which is a superb fuss free belt drive turntable.
I recently acquired a Townshend Elite Rock that had a Mission arm and a Pickering cartridge all for £400 UKP. Truth be told, it's sound is absolutely astonishing, and I am gonna have to try it against my Amazon Model One. I'll be honest - don't spend a penny until you hear the Townshend Turntables!
A very good new deck would be the DPS model 2 - very much a best of all worlds approach
Whatever you do listen to as many decks as you can. All decks sound different, and go with what you enjoy the most.

At 7500 you really have a great choice of decks available to you. Try out a load of decks. You have some very nice Lenco and Garrard variants and you wil lfind they have a superb drive and 'boogie factor'. Direct Drives are very good at being neutral so hear some technics SP10's and similar decks, belt drives IMHO tend to have a wider range of variation - the SME 10 and 20 are very neutral - My own Amazon Model One has a very quiet backdrop and images superbly, although, having recently heard a Lenco variant - I think it doesn't time brilliantly. I personally regret not buying the DPS about 9 years ago when it came out first (I felt that I needed a few more reviewer approvals rather stupidly instead of trusting my ears) the DPS 2 has superb drive and boogie factor and was a rather superb deck for imaging as well. I personally found that the Platine Verier was a tad warm for me.
People tend to appreciate different things in sound, and that tends to change over time. At first I was crazy about imaging, now I am more turned on by timing.
I bought an Amazon Model One. I recently bought an old Townshend Elite Rock for £400 UKP with a Mission Arm and a Pickering XSV cartridge, I am yet to 'face off' against my Amazon Model One, but if truth be told, I have to say I am wondering if the Amazon Model One is as good, let alone better.
I have to say that Roscoeii is giving some excellent advice - listen to a Townshend Turntable before listening to more expensive decks, then listen to it at the end of your audition journey - you may save yourself some serious money.
I will say that budgeting for a good tonearm cable is mighty important. I have a Nordost Tyr, and plugging that in with the Shelter 501, was far better than a Transfiguration Temper V with the TCI cable.

All the criteria you have mentioned buying a good expensive turntable is about functionality, reliability, cost etc...what about sonics ? Anyway a forum like this is highly handicapped to answer big blanket questions like these, on top you dont mention your sonic preferences, in such a situation the only thing you are going to hear is people recommending the TTs that they own or have owned. That would mean every post suggesting a different TT.

My own Amazon Model One has a very quiet backdrop and images superbly, although, having recently heard a Lenco variant - I think it doesn't time brilliantly. I personally regret not buying the DPS about 9 years ago when it came out first (I felt that I needed a few more reviewer approvals rather stupidly instead of trusting my ears) the DPS 2 has superb drive and boogie factor and was a rather superb deck for imaging as well. I personally found that the Platine Verier was a tad warm for me.
People tend to appreciate different things in sound, and that tends to change over time. At first I was crazy about imaging, now I am more turned on by timing.

Lohanimal, interesting that I am on almost a similar boat as you. In the last one year or so, timing of the music has taken up very high priority in my listening. Rather I would say I discovered its importance in the last one year or so. That happened after I heard Naim CDPs and amplifiers and Avid turntables (especially Acutus). Recently I also heard a LP12 with a Naim ARO tonearm and Helikon cartridge and it was again an outstanding performance in terms of speed and timing. Have you heard the Avids and LP12 ? Even a Rega P9 is very good in these aspects.

BTW, I use a Verdier :). But I have made sure I use fast lively tonearms, cartridges and phonostage to go with it and also use a similar rack under it (Hutter). The Verdier times in a different way than the typical British TTs. It doesnt sound blazing fast (like a Rega P9), it is not in any hurry or nervous. It is like a highly skilled sportsman who does everything in a way to make it seem effortless. But then it is an ideal belt drive sound, which will hold its own but still may not beat the Idlers and DDs in areas where they excel. BTW, I have been eyeing a EMT Idler or DD as a second TT to enjoy that sound as well.