I'de say your heads are ok, thickness wise.
I measured the heads off my engine, and the refurbished sets. I am certain the refurb set has been milled too, as the tool marks are visible.
Both sets measured the same.
And above spec, 62.60s and 23.teens
Which tells me I need to check these calipers on some calibration blocks tomorrow. and more about my engine, that the heads were milled at some point.
And as said, on your heads, it's more likely a valve seal is bad, even if it looks ok.

 

I have a 2004 Disco 2 with 80,500 miles on it and the heads are off now. I checked the heads and I have a very very small amount of movement when the heads are set on the block with no gasket in place. The small movement I'm able to detect would not miss-align anything or prevent other parts from bolting on. Good luck!

 

Update - did a vacuum test on the intake ports to make sure the valve stems are sealing. All tested good. Also bore scoped the cylinders and it appears the oil is coming from the bottom end. Will be pulling the engine and disassembling looking for the cause. This will be the second failed rebuild on this motor. One with previous owner and one by me.

I have no idea what the pistons are for this flanged 96mm 3.780 bore so I used rings for that bore and groove size. Assuming the problem is in some way related to this.

I may have to scrap this motor. Too bad, some one invested big bucks in it.

 

So oil is getting past the rings, blow by, but only in one cylinder?

 

All cylinders have oil pooled so assuming all cylinders are same. Compression is good. Engine shop and me have never seen this problem. I’m hoping I installed something wrong but I’m really doubtful especially since this is second rebuild of same problem

 

There are 2 sizes of pistons, A and B, B being slightly larger in diameter.
I have B pistons in mine(and will be replacing with new B pistons).
Machine shop said today my block/crank should be done by friday. Once I get that I can find out the exact bore diameter, and find out if I need to exchange my stock rings. Stock rings that don't specify if they are for A or B pistons, or if the work on both, which I doubt.
I am thinking the B's need +.010 rings.
Time will tell.
May be something you want to check into.

 

Is it smoking out of the tail pipe from burning oil?
Or just on start up, from the pooled oil?
Is it possible the rings are too small, but expand enough from engine heat? But that would be hard to say how the oil got up past the rings once the engine was off and cooled.
Have you done a leak down test yet?

 

Oil control rings installed upside down?
I don't know if they are directional on these engines or not. Some engines are.

 

Not sure if you caught in my posts above, my block has been flange sleeved by previous owner from the stock bore 3.700 to 3.780. No idea what pistons/rings were used. Bores were measured and honed by shop. Nothing found as unusual. I used rings that matched the bore and groove thickness, think they were Ford 4 cyl Hastings rings.

No smoke ever - none at startup, run hard, let off accelerator. The cats are doing an great job but that won’t last. Didn’t do a leak down since my compression is good. Engine runs excellent and is strong....burns obscene amounts of oil

 

I have eliminated all possible oil entry ways from the top end. That leaves the bottom end. It appears the oil is making its way back up into the head from the combustion chamber thru the valve. When it’s turned off, I assume the oil is running down and pooling to the lowest point in the head which is the valve. I haven’t looked on the exhaust valve yet. I have unusually high intake vacuum at 25 inHg. Cam is stock aftermarket so no long duration or high lift. Ring gaps within spec.