Those specs seem pretty nice. The issue you have with the AJA UTAP may not be exactly related. It may be about managing your USB busses.

UTAP does not have an onboard compression engine. It sends an uncompressed YUV stream across the USB 3.0 link.

A single 1080p25 stream is going to be around 1.5 Gbps. While USB 3.0 is rated for 5 Gbps, it's really only stable up to around 4 Gbps. You can probably use 2 UTAPs per USB 3 controller bus.

You need to be sure that you have multiple USB 3 ports, on different controller busses, to be able to connect multiple UTAPs.

Or make use of a faster port, like a TB3 port. A TB3 PCIe enclosure and 1 or 2 multi-port capture cards are a more common solution to what you seek to achieve.

Incidentally, I had a Lenovo X1 Extreme Gen1 for a few week over the summer. Nice machine. Similar to the specs you cite.

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