Dave,

Competent expert who can see your system can help you understand how
your system works; we, at a remove, cannot, except in broadest
generalities.

Thermostat can only control temp of its location. Is it doing that? For
a couple $, you can get various accurate thermometers from hvac-supply
or big-box. The old Honeywell I replaced with programmable has a
thermometer that's close up to about 67 deg F. Then it doesn't move
until temp is above 75 deg F, whereupon it indicates 68 deg F. IOW,
useless.

Other spaces, to be heated controllably, need to be in communication
with system and t-stat. Meaning, for instance, if heated air is pumped
to area of t-stat more so than to other areas, and those other areas
are in poor communication, they will be cooler.

Also, discharges and returns must be designed for consistency from
floor to floor, with heating and a/c. Sometimes kids like to play with
registers, too.

In a different vein:
When you "make" the t-stat, pull the outer cover so you can see the
mercury switch. Do you see the mercury surge to cover the contacts?
The burner should now light. Depending on the setting of the fan
switch, when the heat exchanger warms up to fan-switch set-point, the
fan will start. Later, t-stat will open, burner stop, furnace cool and
fan to off. Easy enough to track this sequence.
When you drop the setting so that the mercury surges the other way, do
you see a small arc as the contacts open?

J