Hi,
Dan Henry wrote:
In case anyone missed my comment here, or did not understand it, or just simply disagree with it, please consider this deeper explanation of the problem in this RTC-like application when not using a timer in an auto-reload mode.

Nope, you may use software-made reload without pay attention on that variable latency and compensations you told about. The trick is somewhere inside your post: advantage of the fact that after Tn overflowed, it continued to count up past zero.
Yeah, you know, you know! (= For example, to count 1/100s without auto-reload mode you just need:
- take crystal 11059200;
- use timer at 16-bit divide mode;
- reload value 0xDC into THx at first lines of timer`s ISR. Do not touch TLx.
It is all...
In case anyone missed my comment here, or did not understand it, or just simply disagree with it, please read yet another time (=
Good days!