I think you're correct in referring to the green cut-to-clear piece (described as a tumbler) - with what the link describes as the standard cut cane/hobnail pattern - as matching as close as possible to the cutting on your vase. However, believe you've looked at the wrong caption/image pairing - the Harvard does appear to be a more complex cut design, with strawberry diamonds and other forms of decoration. I prefer to use the description 'hobnail', rather than 'alternate panels' - I maybe going against tradition, but the expression hobnail does seem to have found much popularity in the U.K., although agree cane is the norm in the States.
Not that the illustrated example being green implies that its history and age suggest identical provenance with your vase - green, red and blue were all fairly common overlay colours - perhaps red and green being the most common - they had a long life and are probably used still.
Unfortunately, for us, this cane/hobnail cutting seems to have been used commonly in Europe and the States, so difficult to date, and equally difficult to attribute. If your vase has known very little use, then it may well be approximately c. 1900 - equally it might be 30 - 50 years later - vases tend not to be cosseted - they're used often and their bases tend to show this.
My opinion is that the widespread use of the this cut pattern, its colour and lack of backstamp mean you may have to live with it being anonymous .............. but it's an attractive piece, has some age, and no doubt cut by a skilled craftsman.