External motor’s connection with the speed of my t

By "adjust the motor" do you mean physically nudging it to keep the belt taut? That's what Dan (and I) took from the wording of your original post.

If you have to do that every day it's not normal. Once my motor is set up right it stays that way for weeks, or until I bump it by mistake! ;-)

It's not unusual for a new drive string to stretch a little from use, but not every day.

A visibly or audibly vibrating motor is not good. I would ask other AS owners if theirs do that. If the table is new, I would report it immediately to the dealer and to AS. You should be covered by the AS warranty and the dealer may have their own refund/exchange policy. The latter may have a short time limit. Don't miss that window if there's any chance you'll need it.

Dan_Ed's explanation sounds right to me and yes, motor slippage is a potential risk on all tables with outboard motors. After all, they won't work unless there's some tension on the belt, which of course tends to pull the motor toward the table. My Teres Reference motor is quite a bit heavier than yours, but it still slips if it's not set it up right. Dealing with this is the (small) price you pay for isolating your plinth, armboard, tonearm and cartridge from motor vibrations.

Putting a different base beneath your TT might help - or it might make matters worse. It depends on whether the top surface of the new base is less slippery or more. IMO there are more important considerations than this when chosing a TT base or stand.

Dan's trick might work. So would a zillion other variations. You just need to increase friction between the motor feet and the surface they're sitting on without introducing so much compliance (aka, sogginess) that you sap dynamics. Nothing more to it than that. Why not experiment and learn? When feasible, I find it effective to try a few DIY fixes to make sure I understood a problem before throwing money at solutions which may or may not help.

I would hate to rig a make shift solution to the problem. After all the money I have spent in the TT set up… It does just not sit right.

Having a nice looking and costly rig like yours is one thing. Getting the best music from it is another. For example, I use a $4K tonearm that's regarded as among the world's most capable. Nevertheless, I've improved its performance by the application of knowledge, experience and 50 cents worth of O-rings from Home Depot. Does that sit right? It does with me. I've learned new things, I've improved the sound of my music, I've shared the joy of those improvements with others.

If your Classic Wood has the standard Rega RB-250 arm, there are innumerable tweaks which will take it to higher levels of performance. The single most effective involves two lead fishing weights and a drop of super glue. They look like hell but no one who's tried them has ever taken them off. Another tweak, which I publicized, involves a paper clip. A third, which I developed, involves those O-rings. If this sort of intimate working with your rig, "doesn't sit right", your rig will always look clean but you'll miss out on alot of great sound, and alot of fun too. YMMV, of course.

Best of luck with your motor,
Doug