If you care about balanced, go with the second option. If you care about basically the best featureset on an all-in-one DAC/AMP, then go for the RME (perfect timing with the new version out now).
Though you have a kilobuck wire... That should be the first thing you get rid of tbh, and then your budget can go with what I went (RME V1 + 789) but your setup would be even better (RME V2 + 887).
If that's a no go, and you want to keep the wire, then just look to getting an adapter plug. (Oh and just for the future, never ever think about taking some other single-ended cable, and try to get an adapter to get it going with balanced.. That's just asking for trouble).
Also, in terms of electrical supplies, if you're at home, that won't be needed. Especially since it looks like you want to use balanced setups, you should be perfectly fine using the power supplies that come with the DAC's/AMP's you get.
Oh btw, if you're not going to go for the RME (since it doesn't offer balanced headphone output, but it is a balanced DAC so you can use a balanced AMP with it in the future perhaps), then consider getting a Sabaj D5 perhaps, it has one of the best DAC sections ever tested on the sight, it will save you a ton of money over the D90.
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Now please understand, the audible difference between any of these setup's is most likely not going to be audible in the slightest (aside from volume naturally). All these devices perform spectacularly. The only actual difference is aesthetic preferences, and convenience, and connectivity, and features.
You could get something like a
Topping DX7 Pro which is an amazing device, and it has the 4.4mm pentacon connector on the front of the device if you don't want to bother trying to get an adapter for you 4.4mm cable. As a DAC/AMP I think it would suit you well. The only downside, is unless you have planar headphones, anything under 60ohms, is going to start messing with the frequency response of the headphone.
Though truth be told, if you don't care about balanced, as I said in my opening statement, you could get a device that performs well, for even far more less. Some of the latest amps have also been the best performers (Geshelli Archel 2 basically the cleanest amp ever tested for under $200).