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then you try to look for a computer with a decent internet speed so that synchronization can run faster (I recommend the VPS / Virtual Private Server)
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uhm, why?
the actual should not be done, it is done when you have a busy job or your computer is restricted in use. I assume the use of VPS, because computers in VPS only you can control without the interference of others
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The way I understand OP they already have a working electrum version, why would they need a different machine for this?
I just assumed only, and should not do 
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Did you ever use electrum? I never had it sync longer than a few seconds.
I'm electrum user. synchronization of electrum indeed is fast ,,, but I experienced anything like MysticTutor,, and by accident on my computer synchronization Electrum very long.if synchronization electrum on your computer takes only a few seconds, I think that because electrum server and your internet connection looks fast