There are quite a few sub questions packed in this post so I'll try to tackle a few of them.
Fisrt the three choice you suggested are in different price universes. The ECM Synchronika is around 3k, the LM around 8k and the Slayer comes in at around 10k. For the amount you will spend on the latter two you can do better these days. You could go for the Synchronika with the available flow control and have essentially the same capabilities at a much cheaper price point. The espresso machine space is evolving rapidly and the LM and Slayer while beautiful machines have become rather dated.
Someone on this thread suggested the Decent. Although I'm not a fan of the aesthetics, it is one of the most progressive machines around. It offers total control of all your variables with the ability to monitor them in real time on a tablet. This machine is evolving quite rapidly and there are a few versions available so to be honest I don't exactly know the price but I believe it's around 5 - 6k.
Another machine with similar features is the Dalla Corte Mina. I have a friend who is testing one at home and he loves it. The software needs some tweaks to improve UX but that should improve. You can also change from their 54mm group to 58mm with a kit offered by the company. I'm partial to 58mm so that's important for me. One drawback is the portafilter and filter baskets are not standard. If they want to become main stream that will need to change. I'm told it also has better temperature stability than the Slayer as well. Priced at around 8k.
I recently upgraded from a five year old HX vibration pump ECM Mechanika IV to the Synchronika with flow control simply because it was in my price range, is very well built and offered the best value for the money. It looks great on my counter and I can play around with flow to my hearts content. The steam capability is very impressive and you can do shot after shot without interruption.
A person on this thread said you cannot plan on an end game here because the game is forever changing and you will eventually want to continue to evolve. I guess it depends on how far down the coffee geek rabbit hole you want to go. Now that's a question only you can answer. At least you now have more info to make that decision. Good luck!
Recommendations for espresso equipment buyers and upgraders.