Hence why I specifically mentioned the E3 series.

Though I was looking at Kaby Lake E3s, specifically, so I will spot you the Coffee Lake H Series could work for the Mac Mini.
I still don't see Mac Mini getting dedicated GPUs - especially if they get hex-core CPUs (i7 or E3) because that will put them square into the iMac 4K and 5K space because, as you note, someone who buys it would buy a nice monitor, as well, so it would directly compete against iMacs (which should have higher margins thanks to the screens).
I'm not looking past the 13" MacBook Pro CPUs for any notional Mini refresh. The
i5-8250U 15W CPU would be fine and would (on paper) outperform every Mini ever released based on Geekbench. Sustained video exporting may be another thing altogether but we can cross that bridge after we reach it - quad core isn't a bad thing to have back on a Mini.
A nicer option would be the
i5-8259U which is a 28w CPU with Iris Plus Graphics 655, 4 cores, 8 threads. It would raise the average selling price of the Mini as 15w CPUs may not be an option due to different CPU sockets used between 15w and 28w CPU apparently. The fact that the MacBook Pro 13" models that use this class of CPU in the 2017 iterations all have the more expensive touch bar I'd suggest that the 15w CPU is more likely.
Weak graphics on the
i5-8250U may not be a problem with the advent of the eGPU and support for it in the most recent macOS. In fact, hobbyists may be able to cobble together quite usable systems if a 2018 Mini came with 2 Thunderbolt 3 ports. Use one for an eGPU and another for external storage (perhaps even an SSD boot disk if a hard drive model was purchased in the first place).
At the top of the notional tree could be the
i5-8300H which uses a different socket again but it's a socket that has a special i7 variant. The i5 has UHD630 graphics, 4 cores, 8 threads, 2.3GHz but a 4GHz turbo which is likely to be sustained for longer with a 45w TDP.
An interesting BTO option would be an
i7-8750H which is 2.2GHz with 6 cores, 12 threads and a 4.1GHz turbo. But clearly this can't happen unless the Mini is going seriously upmarket. This is likely to be paired with a discrete GPU for a most upper end MacBook Pro 15" models - I can't see Apple doing anything for a Mini with this CPU or the i5-8300H.
Going properly upmarket would be to redesign the case - create that highly specified Mac Mini Pro at a high price with something like an
i5-8305g which is far more likely to be a base level MacBook Pro 15" for 2018.