Hi Simon,
The stock TR4A manifold is said to be pretty good flowing and certainly is an option. The two tube design is said to be the most efficient of all the Triumph 4-cylinder designs and better than many OEM exh. manifolds on other makes of cars. But, I don't have any scientific information to support that.
A header is likely to produce a little better, and is pretty much mandatory for use on engines tuned for high rpm performance on the race track. If you were wanting to get every last ounce of power out of the car, with a hot cam, big valves, etc. etc., a header is the only way to go. I'd also recommend a header for any car running Weber side draft carbs.
But, for street cars with a stock to moderately improved engine, that OEM manifold would likely do fine.
I do have a mild steel header on my TR4, installed 25 years ago. It was originally a bit of a project to fit and took some tweaking. That's not uncommon. It was originally chromed and now has a nice patina of surface rust over most of it.
Yes, a header does put more heat under the hood and it's close to the carbs, starter, generator and the brake pipes. I insulated the brake pipes and brake switch wiring (that wiring is probably not a prob on your car, since the brake switch is located differently) with special cloth tubing designed for that purpose and widely available.
On the other hand, the OEM manifold puts some heat under the hood, too. Only a little less than a header will.
In my case, I will be wrapping a new header (on backorder since January!) for more effective temp reductions under the hood of my car. But, the primary purpose for wrapping is really to keep gas temps high inside the header, helping create a more efficient flow.
In fact, with mild steel headers you can only cover 65-70% of the header with wrap. If it were completely wrapped, the internal temps would quickly ruin the header. For that reason, I'm changing to stainless steel which can be wrapped 100%.
Wrap comes in black or white, in 1" and 2" widths and in various length rolls. It should take about 50 feet of 2" to totally cover a TR4/4A header. If you decide to install it, try soaking it in water for a little while to make it easier to install. Special high temp resistant clamps are needed to fasten it in a few key places, too.
There are also available high temp coatings that can be sprayed onto the wrap to help protect it against the elements, you can buy these in typical spray cans. One can is usually sufficient for a 4-cylinder header.
However, even with the sealing coating on it, wrap still will not last forever and needs replacement every so often. It does allow intrusion of water that will be most harmful on cars that are only occasionally driven. Daily drivers will "dry out" the wrap better. In fact, for the same reason, daily drivers are usually fine equipped with a mild steel exhaust systems, while cars that are used only occasionally actually benefit more from a stainless steel system.
Be aware that wrapping a header will void any manufacturer's warranty, but it sounds like the one you have is older anyway, so that may not be an issue.
You also mentioned ceramic coating, and that's a good alternative. It's a great way to clean up an old header that's still sound and usable, or one that's been repaired. It also helps reduce underhood temps, but probably not as much as 100% wrapping would on a stainless header. Ceramic coating would be my choice for mild steel headers.
Ceramic coating coats both the inside and the outside of the header. It also helps promote more efficient gas flow. It's a bit more permanent than wrapping, but will also void any manufacturer's warranties on a newly purchased header.
Most headers avail. for TRs are pretty much as you describe, unless you spend a lot more on something like a Stahl or have a header custom made. The Stahl is probably the top of the line that's still in production for TR2/3/4s, but is only available in uncoated, mild steel and costs about the same or more than a stainless steel header.
Before giving up on the header you've got, I'd suggest having a professional shop look at it and see if they can help match it better to the ports. This would best be done before having any coating or wrapping done, since it may involve some welding and grinding (the one on my TR4 did, when it was first installed).
I don't recommend modifying the head to match the header. Instead modify the header to match the head.
There are also "performance" manifold gaskets, just a little thicker material, that might help mounting and matching the header.
If you aren't sure if your header is mild or stainless steel, a simple test is a magnet. It will attract to mild steel, but not to stainless.
Cheers!
Alan