I'd definitely upgrade. You can get a lot more out of your high end headphones after all.
Granted, I'd do something that you might not even consider; I have experience with every headphone in your signature except for the Auteur and Atticus (but I am a big ZMF fan), and I'd sell every piece of equipment there and get a Stax system. That's what I ended up doing after all. I can elaborate further, but since that's not what this thread is about I'll move on.
With that budget, I'd get a Mjolnir Audio Pure BiPolar amp which is a no-compromise "wire with gain" type of amp, utilizing one of the best amp circuits ever designed (Kevin Gilmore's Dynalo, fully discrete and super linear and transparent) in a balanced configuration (combining two stereo Dynalo amp boards) and combining this with one of the best linear PSU designs ever designed for a headphone amp, the Golden Reference Low Voltage, which measures at under 1 microvolt of noise which is so much better than most of the competition.This PSU is mated with an oversized top notch power transformer and the assembly/build quality of this amp is something to behold.
Likewise the output power of this amp, as high as it is, is pure class A, again unlike most of the competition which has so little class A output power.
This amp also converts single ended input into balanced, so you will need to reterminate all of your headphones with a 4-pin XLR cable.
The only other amp I'd consider actually costs a LOT less than this but should be a stellar matchup for all of those, the Bottlehead Mainline, which can be found fully assembled on ebay and also here on head-fi often, if you don't want to build it yourself. This is under your budget, but it is definitely one of the best headphone tube amps you can get until you get to the extreme price ranges of Apex HiFi Audio amps.
Now for DAC, if you're set on an R2R DAC, I'd try to get a Denafrips Venus instead of the Yggdrasil or Holo Audio Spring DAC level 3. I am actually selling my Denafrips Venus right now for $2,300 if you're interested (
link), and I doubt any R2R DAC under $4k can hope to compete with it. It utilizes four R2R networks per channel, each comprised of 0.005% precision matched resistors and each channel is controlled by an FPGA for decoding - I seriously doubt anything other than TotalDAC and MSB Technology beats this. Resistor matching in an R2R DAC is the biggest issue with R2R DACs, since ideally we'd have much better than even 0.005%, but again I think that is far better than everything except for insanely expensive laboratory grade TotalDAC and MSB Technology DACs.
And four per channel minimizes errors (this type of parallelization is probably the best method, hence why the most expensive R2R DACs have even more) and, combined with its isolated dual mono PSU design with two massive power transformers (Yggdrasil and Spring DAC can't match this neither), makes for a fully balanced DAC. The output stage seems designed around maximum transparency as well, and this DAC has all sorts of input options. It also supports non-oversampling and oversampling mode, so you can use whichever you prefer. The end result is a very smooth sounding DAC, typical for R2R, but without sacrificing detail making it unlike a lot of other R2R DACs.
Source also hardly matters with the Denafrips Venus since it doubles as a top notch digital interface. It converts all other inputs into I2S internally using some of the best chips for this purpose. I can hear no difference with direct USB from my PC, versus I2S from a Singxer SU-1, since the Venus basically does the same thing the SU-1 does.
