The HD598 are a low impedance headphone, I think around 50 ohms. I would look for an amp that has an output of near zero.
I noticed a big jump in soundstage on the HD598 when I moved to a lower ohm amp, so much so that I love the HD598s now, whereas before I didn't get what the big deal was. It is definitely worth it. For example the two tube amps you mention are probably higher in impedance output and don't meet the rule of at least an 8 times difference. I think the Bellari has a 16 ohm output. A tube amp probably matches better with the HD600.
I would recommend the HRT micro streamer over the head streamer if you want something portable. Many like the micro streamer over the music streamer.
The Schiit Magni has an almost zero output impedance, and the Modi is supposed to be very good. I would check with Schiit how the Magni matches up with a very easy to drive headphone like the HD598. You could always consider the Asgard2/Modi combo as the Asgard 2 has a switch for low or high gain. Check Amazon for B-stock. It is the route I have decided to go and I will use the Microstreamer for out and about with a closed set of phones.
Any amp will probably do just fine as the HD598 are very easy to drive but I would try to stick with the impedance rule to maximize performance.