The sensors you listed are switches - they turn on at a certain flux, and turn off at a different flux, and unfortunately unsuitable for our purposes! You need to look for *linear* hall effect sensors.
I searched the site of the onlinestore with the best selection around here. Turns out they have the Allegro brand hallsensors, but they spelled Hall wrong, thus hiding them from a search for Hallsensors..!
Could the A1321 be used instead of the 1301?https://www1.elfa.se/data1/wwwroot/assets/datasheets/07333925.pdf
Get the A1321 if you can as they're the most sensitive that I've seen available - I'm not saying that you can't make a good stick with less sensitive ones (many people do), but I am saying that higher sensitivity gives you more options regarding magnets, placement, distances, and more opportunity to be able to reduce the sensitivity to get the desired response, rather than having to possibly work around less than desired sensitivity. However, the A1321 has been out of production for a while, and I've heard of a number of people who haven't been able to get them. By the way, in the PDF you linked, the sensitivity is on page 5 up the top of the table. The options for the A1321/2/3 are 5, 3.125 and 2.5 mV/G in the "typical" column.