While you are unlikely to be able to identify the uphill trend of such a large area, water is the key to doing so if limited to natural features. It would be difficult to follow water to the absolute highest point in an entire region, but you will at least get to local high points.
As you noted the general slope is very shallow. Local peaks will distort the terrain much more than the region-wide trend in elevation. As other comments and answers suggest, upstream will always lead you to higher elevation. That and other regional trends such as prevailing winds/weather could offer clues. However, these features are also susceptible to local trends misleading you from the regional trend. The key to streamflow is that even the local maxima (headwater of a smaller watershed) area nested within the larger Mississippi River Basin.
As an example of this, consider a quick USGS StreamStats analysis (screenshot below):
In this image the yellow area is the drainage basin flowing into the USGS stream gauge (06887005) near Manhattan, Kansas, and the red line is showing the downslope flow path of a raindrop falling in Denver, Colorado. If you found a stream of any size in this area northwest of Manhattan, Kansas, and you followed it upstream, you would go in the widening, northwest direction of the yellow drainage basin. Importantly, you will reach a local maxima which stops much sooner than Denver.
From that local maxima you can potentially get a view of the surrounding area, and you can try to identify a higher-order stream (meaning a larger stream that has more upland streams converging to contribute to this one). As you follow that one, you will be following a general upward trend.
Here is another screenshot of the boundary between that Manhattan, KS, watershed alongside the flowpath from Denver, CO.
Looking at a terrain map of that area between the local drainage basin and the flowpath to Denver, you can see it is quite flat but it would still bring you next to the higher-order Platte River which you can follow upstream.
If you followed the Platte River upstream, you will spread in one direction of its headwaters, getting an imprecise but general trend upward. If you kept doing this, you would reach a local maxima of the regional basin (e.g. any peaks in SE Wyoming), if not the global maxima (Fishers Peak, CO) of the basin.