The periodic table is just something that makes properties easy to understand/memorize. So, what's going on here is partly an imaging problem, because as you noted, the most common periodic table dumps hydrogen above group I.
Alternatives exist that recticfy some of these issues. I think this one is useful to your current idea:
Although this one has its merits too
Alternatives exist that recticfy some of these issues. I think this one is useful to your current idea:

Although this one has its merits too
