'because I'm still getting extremely foamy pours two and three pours from the first, I don't think heat is the major cause of these problems.'
I think you're right.
If your fridge really is 32 deg. the foaming might be an issue of over-carbonation. Fully saturated, beer at 32 deg/12 PSI will be carbonated to 2.9 volumes (if you're dispensing with pure CO2, which I'm sure you are). Bump this up to 14 PSI for long enough and the carbonation would eventually get over 3.1 vol. At 40 deg. you'd still be at 2.47 and 2.65 vol., respectively, which is not at all inappropriate for some styles, but getting towards the high end if you ask me.
'Is there supposed to be any difference in the reading between the pressure with the shutoff valve turned "off" and "on"'
Only if the system has lost pressure somehow, and you'd hear a hissing of gas and see the needle going back up to where it started as it re-pressurizes. Sounds like your regulator is faulty, as you suggest. Try tapping the gauge, or quickly popping the pressure relief valve open a few times to see if this resets the needle. Fine-tuning it with the valve open might work (see below), but there's probably no reason to think the gauge will read more accurately that way.
It might be best to adjust the regulator pressure based on the flow rate at the tap. Since it's the only variable that's really easily controlled (much more so than accurately changing the temp. of the fridge or the resistance of your beer lines [but also see below on that]), I think adjusting that, even by eye, makes the most sense. See how low you go can while still getting flow, and see if that helps your foaming. This will at first just be due to lower velocity out of the tap but the lower dispense pressure will eventually lead to lower beer carbonation as the liquid and head-space gas pressures equalize (this can take days, especially at cold temps), so you may have to do fiddle up and down to balance flow and carbonation.
As I mentioned before, the setup you have may also just be improperly balanced. Balance in draught terms means applying the right pressure on the keg to overcome the resistance of the system, while maintaining the right carbonation level in the beer. According to the Brewers Association Draught Beer Quality Manual, your tubing alone (PVC, 4.5 ft. @ 3/16th") should give you ~13.5 lb. of resistance, not accounting for other resistance such as from the faucet, or the height of the faucet above the keg. This means you might actually need to apply almost 15PSI to the keg to achieve proper dispense velocity. You may in fact be doing this, if you don't really know what your pressure is set to. 32 deg/15 psi will give you carbonation at almost soft-drink levels (3.2+ vol), and 40 deg/15 psi is still high at almost 2.8 vol. If this is in fact the issue, you'd just have to cut the line down a bit and reattach it to the shank inside the tower, giving you less resistance (shorter line = less resistance) and therefore lessening the pressure you need to apply to the keg, allowing you to maintain a proper carbonation level.
It's always helpful to remember that the carbonation level of a beer is really a matter of only two factors: temperature and pressure. Increasing pressure and decreasing temperature both have the same effect of increasing carbonation, an important factor when trying to get a draught system working just right.
Here's a good chart that illustrates the relationship between temperature and pressure in beer (and is indispensable to me): http://www.zahmnagel.com/LinkClick.aspx?fileticket=HuVGZ8tLaow%3D&tabid=81
Hope that helps.