For most of us the rule of thumb when it comes to budgeting for a system is to put the bulk into your speakers and subs. Like 60 - 70% of the budget. JTR make some pretty kickass speakers and a totally different form factor compared to what you have now, so I'd say you're definitely open to ideas!
I personally think (and quite a few others here will agree) that 4k is an awful lot to spend for amplification. You can achieve much better results shifting the focus (and budget) into the speakers (subs too, they're just big speakers). A good midrange AVR will power most speakers with decent sensitivity to very high spl and sound good doing it. Just make sure it has a full set of preouts so you can add more amplification should you choose to down the road.
I started there, with a good AVR, then got the amp quite a bit later once I got my speakers and subs sorted. And honestly I can't say I noticed any improvements or differences when I added it other than my AVR running much cooler and I started getting braver with the volume... lol. I went into it knowing I was making a superfluous purchase and didn't expect any improvements, but... I wanted an amp!