For your purposes, I recommend either of two portable devices with spectacular performance: the iBasso DX160 DAP for its accuracy and high portability, and the E1DA #9038D USB-C dongle with slightly higher accuracy and even greater portability though it needs your Android phone to plug into. Both of these devices are audibly transparent, and you could carry either one around with you everyday to use with your RE2000 on the go.
Based on iBasso's own measurements, they state that the DX160 achieves a SINAD of 113dB and SNR / dynamic range of 130dB. Seemingly, the independent measurements of the DX160 (2019 version which I own) by HIFIGO using an APX555 analyzer like iBasso's and Amir's
https://hifigo.com/blogs/news/ibasso-dx160-player-testing-report-beat-even-himself
bear out iBasso's measurements and show that the $400 DX160 performs on par with (and with similar output power as) the $3200 Lotoo Paw Gold Touch (LPGT) measured and reviewed by Amir three months ago, receiving the top honor of a golfing panther in its product class:
https://www.audiosciencereview.com/forum/index.php?threads/lotoo-paw-gold-touch-review-dap.18904/
Although, the DX160 seems to have IMD (intermodulation distortion) quite a bit higher than the LPGT. In practice, the DX160's IMD of -94dB should not be audible when playing music, though I wonder if it could account for a pleasant tiny fuzziness or huskiness that I hear in the DX160's sound. You could of course opt for the LPGT instead, which costs eight times as much, runs a proprietary OS instead of the Android 8.1 of the DX160, and uses a full-size SD card slot instead of the microSD slot on the DX160. The Android 8.1 of the DX160 lets you install the music player of your choice if you do not like iBasso's supplied music player.
The $105 E1DA #9038D DAC-amp, which I also own a couple of copies of, has a USB dongle form factor and achieves a SINAD of 115dB or better at 60ohms, and an SNR / dynamic range of 125dBA. It is small in size and most convenient to carry around, but you do need your Android phone with music files or streaming to plug it into. This model will soon be reviewed by Amir, but based on Amir's review of the earlier E1DA #9038S Gen1 USB dongle and on the manufacturer's own careful measurements, the #903D is a stellar performer. Its max power into your 60 ohm RE2000 will be better than 200mW and will be somewhere between 200 and 250 mW, giving you an SPL of 126 to 127dB. This is more than I would ever need with the RE2000, because my average music listening SPL is 70 to 85dB, with peak SPL of 105 to 110dB for brief really loud passages in music.
https://e1dashz.wixsite.com/index/9038d
Review and Measurements of E1DA 9038S BAL Portable DAC & Amp
I could not find the 200mW you quoted on the Hifiman RE2000 product page or on the first page of Google results. From Hifiman's stated specs of 60 ohms impedance and 103dB sensitivity (presumably 103dB at the usual 1mW), 200mW per channel would give you an ear-splitting SPL of 126dB (assuming constant power efficiency). From its single-ended 3.5mm jack, the DX160 with a max 3.2Vrms output would drive 170mw into the RE2000 to give you an SPL of 125dB, and from its balanced 4.4mm jack, the DX160 has a max of 6.4Vrms which will drive 680mW into the RE2000 to give you an ear-shattering SPL of 131dB. To get the balanced output power, you would have to switch the RE2000's cable to a true balanced cable with 2-pin connectors and 4.4mm Pentaconn plug. Please do not use a 4.4mm to 3.5mm adapter with the DX160's bundled cable, as this can damage the DX160's circuitry. The 2020 version of the DX160 available now improves the amp's output buffer to give even more power for low-impedance IEMs.
To use the DX160 with the iLoud MTM, it is better to use the 3.5mm single-ended output in headphone mode to get maximum SINAD from the DX160 at the input voltage sensitivity level of the iLouds, and even then you may have to lower the volume of the DX160 from its max setting. Also, a 3.5mm to dual RCA plugs cable is much more easily available. If the Line Out mode of the DX160's 3.5mm output allows use of volume control, you could use that instead of headphone mode, but likely the LO mode just fixes the output voltage at its max of 3.2Vrms. The E1DA #9038D can be used with the same 3.5mm to RCA cable to connect it to the iLouds. Of course, your Android phone would need be attached to the iLoud MTMs through the #9038D.
