Seeking advice on dealing with possible air trapped in the cooling system

Do this - It's self bleeding.  It's also Carroll Smith approved on GT-40s....

I also have air bleeds from the back of my heads that also go to the Overflow Tank..

Rocky

A self bleeding system is on the docket for future use, but I kinda need the car to be upwardly mobile at the moment to address other issues.

The "system tank" is the shorter of the two tanks, it has two 1³/₈ hoses attached to the side. It should be mounted closest to the engine. The upper hose (inlet) comes from the engine outlet, the lower hose (outlet) attaches to the plumbing that feeds the radiator. That's the tank that should be equipped with a 13 psi radiator cap. This tank serves no other purpose other than to be a convenient place to locate the radiator cap.

The taller tank acts as the coolant recovery tank. There are no connections for the larger 1³/₈ hoses. The overflow hose from the filler neck of the "system  tank" connects to the bottom of this recovery tank. The cap for this tank should allow the tank to be vented to atmosphere.

If the cooling system lacks the "head tank revision" as detailed in Chuck's (Rocky's) drawing, then the left hand tank of the radiator should have a petcock screwed into the fitting located in the top of the tank, making it possible for you to vent air from the radiator manually.

Start the engine, keep the recovery tank half full, leave the cap off. Turn the cabin heater on for full heat (this purges air from the heater core).  Once the engine reaches operating temp raising the front of the car will help any air in the engine or the plumbing downstream of the engine to flow towards the radiator; then raising the rear of the car will help any air in the radiator outlet flow towards the engine; then raising the front of the car again shall help any remaining air flow towards the radiator. At this point all the air in the system should be in the top of the radiator, opening the petcock in the top of the left hand radiator tank should allow that air to flow out.

Keep the level of the recovery tank about ¹/₂ full when the engine has cooled to ambient temperature.

P.S. whimsical note from the forum admin. You did an excellent job titling the topic and selecting the forum!

@George P Just to clarify, am I supposed to raise and lower the car at either end as directed, with the engine running? Or can this be done with the engine off after coolant has reached 160-170F? I'm pretty OCD about shop safety and the idea of lifting the car on a floor jack while it's running doesn't feel "right" to me, even with the large rubber wheel blocks I use. But hey, if this is the way it's done, then I'll do it. I just want to be absolutely sure, as it's a sizeable investment I have in this car on just the purchase price alone, not to mention the current work done and future changes I plan on making to the car.

Regarding the topic title and forum selection, I noticed that a couple of my past posts have been modified, so I figured there was a specific format we're supposed to adhere to.

Thank you (and to everyone else responding) for your responses to my incessant questions regarding this car. While I'm fairly mechanically inclined and have done all of the major work on my Shelby GT500 and Focus RS, the Pantera is a substantially different animal (pun intended) than what I'm used to.

yes, leave the engine running, keep the coolant circulating, and the air along with it.

I normally leave the pressure cap off the system tank, and watch the coolant level in the tank. If it decreases I'll top it off, but at some point (when the thermostat opens) the coolant will begin overflowing the tank. At that point I screw the pressure cap on. At that point I also know that the thermostat has opened, and that it is time to raise the front of the car for the first time. 

By all means keep at least one tire chocked on both sides, to prevent the car from rolling forwards or backwards.

Click on the link to "my Pantera's photo page" and read my notes near the bottom regarding the coolant system. Pay attention to the part about the plumbing between the radiator outlet and the coolant pump inlet.

...It is My Opinion, Air in the System is Not Your Problem! Your Problem is, The 'Radiator' cap is NOT holding the PRESSURE. Not even close! I Run a 16 LB Cap. I've never done the 'raise the front, raise the rear'. Never had to. I just bleed the air out, at the Top Left corner of the Radiator. Nor, have I done the 'Hosed System Re-Route', Modification.

Most important is to have the 'Pressure Tank' (the Short One) Raised up Higher, with the Top Most Level of Coolant 3 Inches Higher than the Top of the Valve covers (See in Pic). This gives a 'Highest Chamber' for All air to Accumulate. And where the Air will be 'Burped-Out' into the Recovery tank, BEFORE the coolant. Then Upon Cooling Down, the Correct Cap is Designed to Allow a Reverse Flow of Coolant from the Recovery Tank Back into the Pressure Tank...FREE of Air.

If I should open the Cap on the Short Tank...When all is Cold, Coolant spills-Out, as there is NO Air in the Tank, at all, Because the Recovery system from the Over-Flow Tank, is working Perfectly. The Caps on Your Tanks May Not Do This.

The Sounds You are Hearing are Coolant Boiling into STEAM, because the System can Not hold the Pressure, which would PREVENT This from Happening. Last...all that 'Mud' spilling out of the CAP, Should Tell  You, the System needs a Complete 'Flush-Out'. And then, get some 'Anti-Boil' mixed in Distilled Water (NOT DE-Ionized Water!) 50%-50%. I do a Ratio of Aprox. 40% Glycol-60% Water.

MJ

P.S. Double Clamp Every Hose End, Just a Recommendation, this will save You a lot of Heartache in the Future. 

Well I found out why I'm barfing the coolant out all over the place and I am really embarrassed. It would probably help matters if the radiator cap was actually twisted all the way so it's tight. So much for being "fairly mechanically inclined".