Please check exactly which type of files are supported by each device. Korg models do not do FLAC - and only MR-1 does MP3. None of the Korg can play any file unless it is on its internal hard disk - you can not use it as DAC with PC.
This was the Aichille's heel of Korg and what ultimately took it off the market.
Checking Tascam DA-3000 http://tascam.com/product/da-3000/ reveals it can not do FLAC or MP3. It can be used as A/D and D/A converter with PC. You can covert DSD to PCM (be it WAV, FLAC, MP3 or whatever ) using Korg Audiogate. This has been unfortunately limited for non owners of Korg MR product. After discontnuation of MR recorders Audiogate went from V 2.x.x to V.3.0. and beyond. That is a PLAYER first ( meant for Korg DSD capable DACs ) with enhanced sound quality over V.2x.x. However, if you require any "editing", V.2x.x is MUCH more user friendly for editing purposes, like recording from LP. V.2.latest version should still be available for download somewhere at the bottom page after downloading latest version. Only you can decide whether or not buying a Korg MR product (or DAC) is worth it in order to get the full access to Audigate.
There are other "converter" softwares available, like Weiss, but that co$ts several times more than the DA-3000 itself.
What I would do in your shoes would be to get DA-3000 and use player like JRiver 19 that can convert files from say MP3 and FLAC to WAV or DSD on the fly provided your PC is fast enough. One caution in this case; not only should PC be powerful/fast enough, it should not impersonate tornado in your listening space; usually, when called upon load as difficult as conversion on the fly, fan(s) do kick in. You can download trial version of JRiver 19 and test it with your equipment and your requirements - but you will need DSD capable DAC to test it to the full. If you do have PCM only capable DAC , you can still test conversion on the fly for "tornado" in somewhat limited edition.
You can use DA-3000 as a standalone unit. However, as good as it is, why listen to an analog source trough A/D and back to D/A conversions? Only needed during the recording, pure listening to vinyl should be that - left pure. Please also remember some ( well most, but not all ) recorders of any kind
can present an awfully difficult load to the source driving it ( in your case phono preamp ) when switched off. It ranges from just faintly audible to heavily objectionable - depending on actual hardware combinations. Some preamps use tape out buffers, some use recording selector that can be switched to off. If you use only external phono preamp without any switching capabilities, disconnecting the recorder
anytime it is not powered on while simply listening to vinyl will be required.
Good luck !
PS: If you are content with only PCM limited to 96/24 and require portable no frills device, a Sony PCM M10 offers just that. No fancy or hard to get batteries and storage media. But do not think it can be used as an outboard A/D and D/A with PC.