I think quite a bit of your problem is "self-inflicted injury".
I've had to install a fan to remove the hot air from inside the rack, and although that's worked well for several years, it's been giving me problems again. I've now drilled holes in the side of the rack to allow hot air out the side. I also got a top panel that I drilled a few hundred holes in to get more air moving inside the amp chassis, and allow more hot air to exit the amp.
might not be a good idea (see below)
The amp is completely and totally unreliable. This amp has failed on me in less than an hour, and provided plenty of instances of me being completely embarrassed because my big, fancy pants expensive amp shut down on me.
The heat sinks are the long, rectangular things- the fan is directly to the right. The idea is that the fan will passively draw air from the back grate (top center), push the air through the heat sinks towards the exit grate to the left.
What problems does this present?
The air inside the chassis is heated by 3 things. The transformer (front right), the preamp tube (front left) and the heat sinks. The fan is pushing hot air through the heat sinks to cool the amp. Think about that. Hot air, cooling the amp.
You say "passively", but a fan would be "active" I think....... The design your amp shows is very standard, and is not an inherent problem as far as general setup.
The amount of heat provided by the small tubes is minimal. It would not be an issue if the total volume of cooling air is sufficient. (see below).
The TRANSFORMER is a slightly more visible issue. The design, long and thin, is inherently inefficient, because there is a lot of "length per turn", leading to added resistance and more heating. If the amp shuts down for 10 minutes at a time, it may be due to insufficient cooling of the transformer. There should be air vents to allow air to pass around it and cool it. (see below). A toroid would run cooler and shut down from transformer overheating less often.
Also, the distance apparent between the heatsink and the chassis wall does, as you mention, allow recirculation of hot air. That will be worse if the exit of hot air is blocked. It is better to have no more than 6mm or so space, and to align the holes in the chassis with the heatsink fin spacing.
The amp is designed to be rack mounted. The front panel of the amp is designed to secure the amp to a rack. It's recommended in the user's manual to rack mount the amp. I have the amp mounted in an SKB rack. The wall of the rack is around a half-inch from the wall of the chassis. Because it's so close to the exit grille of the amp- it's resistance to the hot air that does exit out of the grille. The air that doesn't dissipate from the wall of the rack gets pushed back into the chassis of the amp. Because there's about an inch between the chassis wall and the heat sink, that hot air is able to get back into and get recirculated through the heat sink.
But remember that the amp passively draws air into the amp. If the heated air gets out out of the heat sink, and out of the chassis, it's enclosed in the rack, and THAT air is drawn back into the amp.
SKB (Shoulda Known Better?) racks are notorious for fitting like a glove, which is bad for cooling. They aren't any bigger than they absolutely have to be to fit the equipment.
With only a half inch to the wall of the rack, you are essentially totally blocking airflow. I would be pretty sure that the manual mentions that you should NOT block airflow..... but you did.
The mere fact that it can be rack mounted, and SKB is a rack, does not necessarily mean it should work perfectly in an SKB rack.
The incoming air vent on the back is actually fine. It should be able to draw in cooler air because the back is open when in use. (you DO at least open the back in use, right?) If sufficient airspace is available for the air to leave the chassis out the vent, hot air should be rising away from the chassis, allowing cooler air to come in.
You keep saying "passively", but in fact the fan is blowing air OUT actively, so air will be actively sucked in through the other vents. The positioning of those vents then can direct airflow over any other parts (transformer) that need cooling. The general airflow should sufficiently cool the small tubes in preamp.
it is possible that the large inlet vent in the back does not sufficiently cool the transformer, OR that your "total enclosure" rack does not allow airflow into the vents that ARE by the transformer.
Drilling a lot of holes in the amp top at random has several problems.
1) it lets the hottest air, that has already risen away from the chassis, back in.
2) If the original vent system would have sufficiently cooled the transformer etc if air was not blocked by the rack, your extra holes have completely messed up that system. If you drilled them all near the transformer, it might not be so bad, aside from item 1.
The real question is whether the amp will work OK if it is NOT covered up by a tight-fitting rack. If so, then your problem is the rack, and you should provide venting of the rack to fix it.
If NOT, then you may have a point. But I suspect that the unit will do what you want with no problems when allowed to vent its heat.
Venting the rack right in line with the heatsink air exit would be a really good idea.
I agree that a weakness of the unit is the space between the heatsink and the chassis wall. That alone makes it over-sensitive to vent blocking, as it does allow recirculation.
You could, since you have already been in the unit, add some side baffles between the heatsink and the chassis wall to direct that air right out the side and not allow it to re-circulate. That alone might fix a number of your issues.
Then cover up all the holes you put in the top....... unless they are by the transformer, AND there are none in the side by it.