Get a Multiview 4 and a Hyperdeck Mini.
Put your 4 1080 feeds into the MV4 and output at 2160. Then record at 4K on the Hyperdeck.
The downside is that the 1080 extracted feeds will only be progressive.
You can also use a Teranex AV to realtime playback and see all 4 sources as separate feeds @1080, because it has simultaneous 4 way split outputs.
Baz