Your furnace is shutting down on limit. There can be a number of causes for this.
Start by making sure you have a clean filter in the furnace. A dirty or restrictive filter can cause this issue. Alternatively you could also have a dirty or plugged up A/C evaporator coil which is located above your furnace. This can also cause a furnace to cycle off on high limit, however is uncommon unless you have run your furnace without a filter for prolonged periods of time. Also if you have a high efficiency furnace, there is more of a chance to have the secondary heat exchanger plug up rather than the A/C coil.
You can also have a blower motor issue. The motor can be faulty or seizing up causing it to not spin fast enough to move enough air through the furnace. Another cause may be that you have a faulty limit that is opening prematurely.
The major issue that can cause this problem is a heat exchanger issue. If your furnace is cycling off on high limit, and everything checks out, you may have an internal blockage of the heat exchanger. If this is the case either the heat exchanger or the furnace will need to be replaced. A combustion analysis of the furnace is required to prove this is the issue.
If you happen to have a 2 stage high efficiency furnace you could have a bad ventor motor gasket which is allowing air to be drawn in behind the motor. Big cracks in the condensate collector pan can also cause this but is very uncommon. You can also have the a two stage gas valve high fire solenoid stuck open, but this is also very uncommon and can only happen on 2 stage furnaces. Also if you have a bryant, payne, or carrier high efficiency, you could have a cold spot baffle leakage that is allowing air to be drawn in between the primary and secondary heat exchanger however this is also very uncommon.
If you think your blower is not spinning fast enough you may also have a bad blower motor, or if an ecm motor, the control board may be bad. If its a fixed speed motor and your getting power to it but its not spinning fast enough it could possibly be a bad blower motor. If you decide to change out the blower motor, make sure to get the appropriate replacement capacitor to go with it. I actually did have the same issue on an older carrier high efficiency furnace a few weeks back. It ended up being a bad blower motor, however the motor spun freely and had no indications of seizing or hard starting.
Does the ratio of static pressures between two stories differ at different blower speeds? That's a very interesting question, but I believe it's a moot point. Any dramatic difference would mean your system isn't balanced correctly in the first place. (needs zoning, split systems, or an actual balancing)
Stack effect will cause plenty of heat to go upstairs, while the cold air will settle. I'd be more concerned that it won't cool right. Except that furnaces usually only run at high speed for AC because cold air is denser, making it harder to push. If your old system heats and cools just fine I don't foresee a problem.
Without being in the correct centralized location (which is somewhere on the first floor of a two story), the thermostat will not control the house properly. In low-fire mode, indeed less air will go upstairs and downstairs, per minute. Blowing softly is what makes it more comfortable. It will run longer and more often, reducing the intermittent temperature differential, keeping the house nice and even.
So no, the same amount of 'less' air will be coming out below as above. Your contractor either is trying to up-sell you into a split system (or knows more than I do) or convince you that zoning is required (a possibility, however this can be retrofitted later at your discretion). Either of these additions would dramatically increase the cost.
Unless your house has automatic zoning and was balanced by a genius, it will always be hotter on the second floor in the winter, and colder on the first in the summer, just like everyone else's.
Best Answer
Empirical Engineering Answers:
Yes: you will save electricity costs by running your blower on low.
No: you will not save on gas/oil costs by running your blower on low. Because the slower air velocity over the heat element is transferring fewer BTU units into the circulated air and they simply go up the exhaust pipe.
The NET difference of the above two figures is your savings or cost.
I am currently heavily invested in studying and learning the subject as I commit myself to reducing my winter energy costs this year.
With heating oil at $4.50/gal I can assure you without measuring anything that running my blower on low is NOT more efficient from a $$ perspective. I'm in the process of re-wiring my blower to run on high with the furnace. In support of this: I found the mfr owner's manual for my furnace and in it, it states, "if you have an air-conditioning coil installed, you should switch the furnace blower speed to high to accommodate the decreased air-flow caused by the cooling coil in the plenum."
I have also measured that on low speed my furnace requires AT-LEAST 1 hour of constant running to raise my home temp by 6 deg F. On high speed it takes 30-40 min. With a one-gallon-per-hour burner nozzle that saves me AT-LEAST 30% on fuel oil plus another 20-30 min of blower run time or at least 30-50% run time savings. Now, I haven't done the measurement to learn how much electricity my blower uses on low vs high. But I'm reasonably sure it uses less to run on high vs low then it uses to run on low vs OFF. I do know that my entire furnace runs safely on a 15amp breaker with the blower on high, the burner running, the humidifier running, and the water pump to empty the humidifier running. Thus, my blower can't be using that much electricity on high.
So clearly, running your furnace blower on low is only more efficient IF-and-ONLY-IF the cost of the heating fuel is much much less then the cost of the electricity to run the blower that little bit faster.