Frank - My 15m steel motor cruiser was taken from Strasbourg to Basel by a co-owner in early June last year. Levana is about 22 tons but overpowered with a 210 hp engine. The co-owner used the Rhone au Rhin Noord Branche, then 90 km on the Rhine / Grand Alsace. He reported a number of issues that need to be considered. He said it was "very hard going" with huge fuel consumption and moorings in Basel were pretty scary with having commercials mooring nearby and getting into a free spot with the high rate of water flow was very tricky indeed. There's no nice sheltered marina in Basel.
However you have only 19 km of Rhine so I'm sure perfectly doable with your boat, but not when the river is flowing fast. Navigo reckons that motoring at 10 kph through the water, the trip would take about 4 hours with an adverse flow rate of 4 kph. It's often nearer 7 which would double your travel time.
Later in September last year, I took Levana 650 km down the Rhine from Strasbourg to near Den Bosch in Netherlands (see latest Blue Flag) and I certainly didn't envy those few brave souls going upstream.
Don't let me put you off though, but personally I'd look at a much easier alternative if you want to visit Basel - I believe it's well worth visiting even just for the energy-free (no engine, no sail, no oars) ferries that ply across the river. I'd stop at Mulhouse on the Rhone au Rhin and get a direct train to Basel - takes 22 mins, runs every 15 mins or so, costs about €15 and the last train back is at about 22.30. Simple, but you won't have the opportunity to fly the Swiss courtesy flag you bought specially for your Basel visit!