Do you have a push bar as well???
Most tow bars I've seen for light singles don't work very well pushing an airplane up a slight incline like the OP described.
If you are really concerned, you could do it like I do in the twin - straighten the nosewheel with the bar and then push on the inboard leading edge....pain in the behind because you have to keep going back and forth adjusting the nosewheel.
Mine has a rod that goes through the nosewheel axle. Works in either direction. I, too, have an incline in front of the hangar. And a plane with a 2200lb empty weight and 90 gallon fuel tanks. Do I push on the prop...yes, occasionally, but I try minimize it as I really don't like the idea of doing so. And I do occasionally have someone help by pushing on the leading edge as long they understand to push on a rivet line.
It's not like you have no alternative. Even taildraggers have options available to them.
The universal towbars such as those that are manufactured by Brackett work in tension and compression. They have a positive clamping action that will not disengage until you release it.
Several different powered towbars available use various installation schemes, but for the most part they involve some positive means of attachment or utilize the weight of the aircraft to maintain attachment and work in either direction.
I've written Santa several times to deliver a powered towbar, but, to date, he's not responding to any of my requests. One day my back will give out and then the issue will be settled.
The towbars such as those supplied by Cessna and Piper are too flimsy to be relied upon in my experience. I've had them disengage while in use due to their susceptibility to slippage, distortion and breakage even when only used for pulling. But a lot of people use them.
As far as flight loads vs. ground handling... how many fatigue cycles is your flange good for? What forces are the flange and front main bearing designed for? It comes down to risk management and I find it more comfortable to minimize unanalyzed conditions. Others may feel differently and that is their prerogative.