Is it a hire boat? If not, then you can plan your trip to avoid busy periods, for example (several times) we went up Grindley Brook at sunset and had a straight run through. Or New Marton. Those are the worst congestion areas, although TBH I like the bustle of meeting lots of other boaters.
If you are restricting yourself to 8h/day in June then from Nantwich you'll probably only get to Trevor and back - which is good, but misses out the best (IMHO) section which is Trevor - Llangollen Basin. Sure, there's the Ponty aqueduct but also there is the Chirk aqueduct, I don't like heights so prefer Chirk (or none at all).
If you've never done it, Llangollen Canal is well worth doing, much better than Shroppie southbound out-back. But Nantwich offers decent cruising opportunities, there's Anderton-rtn and Chester-rtn too. I would rate them:
1. Trevor-rtn
2. Chester-rtn
3. Aldersley Jn - rtn (the trip if you go down the Shroppie, then go a little along the Staffs & Worcs then turn at that junction - you could moor then walk up a lock or two of the BCN).
4. Anderton-rtn
If you can extend 4 days to a week; or are okay with longer days, each route could be meaningfully extended to Llangollen; Ellesmere Port; Stourton Jn; going on the Weaver respectively. I have lived and have a boat moored in the local area for 10+ years, so have done those trips dozens of times so its coming from (recent) experience.