DJM-450 and Tascam Audio Interface

To cut quite a long story short - I currently use a Reloop mixer (chosen based on a space constraint) and I have for many years (on various DJ setups at home and in clubs) used a Tascam DR-05 to record sets. I have recently noticed some issues with the cleanness of recordings when using available RCA outputs on the Reloop so now I'm looking for a better solution.

(For anyone out there considering a Reloop RMX, I'm experiencing a pretty significant bleed from the headphones onto recordings, which from a DJ's perspective is a cardinal sin. I'm yet to hear anything back from Reloop on it.)

With my XLR outputs taken up by my speakers and now being quite suspicious of any RCA outputs that aren't REC OUT, I'm considering buying a DJM-450 specifically to make use of the USB Audio Interface for recording. Other models of Tascam such as the DR-05X and DR-07X have their own USB audio interfaces which use ASIO drivers to record the output of PCs and laptops.

But the Tascam manuals specifically show options to connect the interface to PC/Mac or iOS, so I'm not convinced these will work with a DJM-450.

Is anyone able to say categorically that this will or won't work?

I don't have a personal laptop available to do recording by the way. I don't have an iOS phone. And I'm also quite limited by space which is why a Tascam is ideal for capture. I have a QNAP drive that is relatively close to the mixer but I see no information at all online about the possibility of audio capture using ASIO on QTS.

Thanks.