My guess, and a strong one in fact, is that we'll probably see HCA after HBZ. Seeing that the $5 bill is the only likelihood of seeing denominational letter C, since the earliest recycled letter for the $10 is F, and the earliest for the $20 (after Z) is L. Given that they recycled L, R and U for the $20, and reverted back to I afterwards, it wouldn't shock me if C is next after HBZ.
Of course, the $10 bill did recycle F (formerly on the $1 bill, and enjoyed a very, very small limited run on the final 1975 $50's), but again, the $10 denominational letter F was incomplete (it only got as far as BFW), so we won't know for many, many years if we will see what will come after FFZ, if we'll be seeing FGA, or if we will see GDA. I think that if the $5 HC* series gets exhausted before the $10 FF* series, denominational letter G will likely appear on the $5, and if true, we may see FJA-FJZ or GDA-GDZ on the $10 (denominational letter J is, most likely, retired from the $100, but can likely appear on the $5 or $10, if anything.
Of course, just because letter I is not used as a third letter, doesn't mean it's not used on serial numbers. The letter I is still seen on the $20s as a denominational letter, so that's an indicator that we may likely be seeing INA-INZ after the printer letter H runs its course. Then again, maybe by that time, we may end up seeing $5 coins.