Andrew,
My take on your overheating problems is “yes” to all the above..

First off, I assume you like me did NOT do an initial run in procedure to “break in” the bearings. Information I found when I had to replace the bearings on my mill/drill was:

” Typical run in for spindles is a starting point of about 400 rpm,
up to max in 500 rpm increments, in steps of 30 - 45 minutes.
Check housings for excessive heat as you go.
Then reverse and do it over!
Watch temperature. If it gets hot, stop let cool and do over.

The Fafnir Superprecision Machine Tool Bearing catalog suggests that with optimal design,
bearings running synthetic low friction grease ought to be able to run about 20 degrees C
over ambient or about 40 degrees F. In fact, they suggest a proper break-in procedure temperature of 130 degrees F.
involves running the spindle until it reaches 150 degrees F, turning it off to cool, and repeating the cycle
until the spindle stabilizes at 130 degrees F or lower operating temp.
The ideal equilibrium operating temperature is 95 to 115 degrees F. Maximum temperatures should not exceed
170 degrees F. Timken's published specs for tapered roller bearings, including bearing life specs, assume an operating
temperature of 130 degrees F.”

To this end, I got one of those cheap non contact thermometers off e-bay and proceeded to make runs at various speeds and when the temp got up, stopped and waited for it to cool off and repeat. I was surprised as to how the max temps dropped quite quickly. As I say, I had never done a proper breaking on my machine and up until the day the bearings tore up, I had high temp problems. When I increased the max spindle speed to 4000 rpm, it got worse.
Next thing, is to use a proper grease NOT wheel bearing grease as it is to thick. A lot of people recommend Kluber 15 and only fill to about ~30% as I remember. To much grease will also cause more heating problems.

Preload can also be a problem and trying to get it set up properly can also be a pain.
When I did my quill, I set it up in the lathe so I could easily adjust the preload before putting the quill back into the mill. This also gave me several additional rpms to ramp up the speeds. The other thing I did, was to setup a spreadsheet and recorded all of the various speeds, temps, etc. The good news is having 4000 rpm at a max of 135° F (~57°C)

As to the problem of seals, my machine has no direct contact seals on either the top or the bottom bearings. I feel sure that at these kind of rpm, this could also cause a problem.

Hope this helps.