A turntable should not add ANYTHING to the sound quality. The most important attributes a turntable can have are lack of noise, isolation from the outside world, pitch consistency and speed accuracy. Pitch consistency requires unwavering speed and a very flat record. So, the turntable must be able to clamp the record flat.
Going to another idler drive will do absolutely nothing for you. Remember, the sound of your friend's system was due in the most part to his Speaker/room combination not the turntable. You already have a fine set up with one exception, the Garrard. @clearthinker is absolutely right. Idler wheel drive is an antiquated design. The noise and rumble are legion. Each bearing and contact point adds to the symphony and on top of that their pitch consistency is poor. The attraction to these turntables is purely psychological. Like clearthinker I sold my last idler wheel drive table in 1967, never to look back.
On the bright side there are meaningful improvements you can make by going to a quieter, more accurate table with isolation and either vacuum or reflex clamping. Sota is out because your arm will not fit. SME is a possibility if you can find one you can afford. The Kuzma Ref 2 is an excellent choice and in your price bracket! Get a good dust cover for it and you are in business. You will notice my blacker backgrounds and a realness to the music missing in setups with poor pitch consistency. Wavering pitch kills the illusion that you might be listening to a real performance.