I think your houserules are fine. I have used shorter check intervals without experiencing any problems, as long as the intervals are long enough for the players to have a reasonable chance to do something about the disease.

I wouldn't use a random number of checks per day because it does not tell you the interval between checks. I would make it a fixed 4 hour interval, or maybe every 2d4-1 hours if you really want randomness.

Interesting choice to start the disease with a buff instead of a debuff. That will lure your players into not thinking this is a disease; whether that is fair or not depends on your playstyle. You seem to be implying that failing to identify the disease makes it harder to cure (although that is not refected in the entry). Assuming that to be true, and given that stage 1 is a red herring, and the fact the players don't get a full day between stages of the disease, I think your DCs to identify are too high to identify it. I mean, the DC at stage 1 is Hard+4, that's a bit over the top.

Your maintain/improve DCs are also too high for a level 4 disease. Maintain DC should be Easy (DC 10), improve DC should be Moderate (D 14).

I think the general rule for creating diseases is to make stage 1 a minor debuff; stage 2 a moderate to serious debuff; and stage 3 or 4 anything up to and including fatality.