I just bought a real nice pair of SL3's a few weeks ago. I was driving them with a restored Bose 1801 amp (500+watts into 4 ohms) on the woofers and a Pioneer Spec 2 on the panels. Better yet but obviously much more expensive, grab a XPA-2 for the woofers - I would guess the UPA would do just fine tho unless you are trying to break windows
Yesterday I got a Mingda MC34AB amp for the panels, using the Spec 2 for the woofers........wow - it really is impressive. While the other system sounded really good, with the Mingda it is just so darn life like, detail and clarity like I have never heard before (admittedly I have not heard a lot of real high end systems so I am sure I am still in the budget category).
so my suggestion would be, depending on how much you want to spend, to get an Emotiva UPA-2 ($349) for the woofers and something else for the panels.
I obviously strongly prefer tubes now and the Chinese make some awesome gear at pretty much any price point you want.
You could get something like the Mingda MC34AB (is what I have now so I am biased) because it is a power amp and an integrated amp. (around $1400 shipped)
I thought my Conrad Johnson tube preamp was much better then the Mingda, so later on, you could upgrade to a different preamp if you liked. But the Mingda would work until you did. I can pretty much guarantee the Mingda will sound better then what you are using now (tho obviously we all listen for different things and you may not even like what I like)
Total cost for both would be around $1600 - I know it is expensive, but what a difference you would hear. You could do it in stages to make it cheaper. maybe get the Mingda and just use it until you got the Emotiva - I tried it alone and it was more then powerful enough to drive the SL3.
Cheaper yet you could try a Yaqin MC10L or MC20L - I have heard nothing but good things about those. They run under $500, so you could get one of those, but it is an integrated amp only. I believe later on you could just use the AUX jack with the volume turned all of the way up to use it as a power amp. You would need a preamp later.
Just my opinion and ymmv and my ears could be tin - the SL3 is capable of putting out some serious music and does show the down line flaws in the system; so build the system in stages. May take you a little longer to get there, but my ears have never been happier.
I will also say that I am a 2 channel music guy, so I have no interest in HDMI outputs etc, which could make a big difference in what you use yours for.
I do know that while I always thought I had pretty good systems, I never thought I would own a system that sounded as good as I have now......I am loving it