There is more to be aware of in the connection issue than "just making a connection:
I've read a helpful post that outlines a few connection methods, such as high temp solder, adhesives, and constant mechanical force, but none of those appeal to me.
That's a useful article and worth reading by anyone wishing to use thermocouples for measuring small low mass temperature sources BUT it is not principally aimed at electrically connecting the thermocouple to the measurement system - it's mainly about connecting the thermocouple thermally to the target heat source.The two tasks have quite different requirements.
I have read that it is possible to solder a Type T thermocouple, but this requires a fairly expensive thermocouple (I found them for about $70),
Type T thermocouples are Copper-Constantan. You can make your own from two wires of the appropriate sort, spot welded at the tip. Price can be under a dollar for tye actual thermocouple. Add sleeving, handle and beautification to increase price as desired. It is possible to but rolls of thermocouple wire which use the correct materials and which are intended for extending the thermocuople connecting lead. A length of this wire may be cut off, the end spot welded and a thermocouple produced at very low cost.
BUT soldering this material MAY produce problems if not allowed for - see below.
Cold junction issues:
It is crucial to realise (and you probably do) that the conductive materials used in the connector for a thermocouple will influence the result as they form a second thermocouple at ambient temperature.
Knowing both the ambient temperature at the point of connection and the materials used is required for "cold junction compensation". If you just solder the wires to eg a PCB or to some other wires (copper or tinned copper or ...) you will introduce differing metal-metal connections in each case and the low temperature thermocouples formed will be different, and probably unknown with any precision.
This is one reason why the tip of the thermocouple where the two wires join is usually welded rasther than soldered or brazed. Quite apart from melting point issues, introduction of another, or several other metals in a solder or brazed mix will create a new thermocouple of unknown characteristic.
Can anyone suggest other options? I would have just bought Ryan McLaughlin's Single Thermocouple Interface since it's exactly what I need
Ryan's interface is "more real" than may be obvious. As it notes in passing " ... while also using the proper metals in the connector required for a thermocouple connection ... " - ie, he knows his stuff. Additionally, the converter IC involved is located on the same PCB as the thermocouple socket so any additional junctions formed by track to IC pin transitions are (approximately) balanced in both leads and so any potentials generated are invisible to the system.
There are a number of connectors on the market which may suit you but, whatever is used must address the "correct connector materials" and "equal materials in both paths " issues.
The RS socket that you mention could be sent to you from afar off - and RS will send internationally if suitably encouraged.
Omega have a range of potentially suitable products and here and also here and this wire-wire connector of theirs looks adaptable to your purpose and seems to be available in 1's.
Here is a useful discussion of the low temperataure juntion issues that I mentioned above
comment in poassing on the same issues
BUT regardless of what you use - something from above or elsewhere,
you will need to be certain not to introduce extra "junctions" into the connection path
OR to introduce the same ones in both legs
OR be aware of what extra junctions are and how to allow for them
AND to be aware that soldering may cause differences.
If soldered, any connector you use will ideally use the same leg material into the PCB.
A thermocouple is made from two different conductors in contact - frequently welded, but twisting together will work too.
A type K thermocouple is made with chromel and alumel conductors. There are many types of thermocouple, designated by different letters, and using different metals. See the Wikipedia article on thermocouples, or do a web search for "thermocouple types" for more information.
Best Answer
Thermocouples create a measurable voltage difference given a thermal energy difference*. This is the Seebeck effect. A "K-Type" thermocouple uses a particular alloy combination which is, as the Wikipedia article states, a general purpose design that varies widely because technology has advanced since its inception.
Specifically:
(emphasis mine)
Therefore, K-type alloys can measure up to 1350°C but not all products are designed with this upper limit in mind.
As Nick pointed out in a comment, you can find thermocouples designed for high temperature. For example, the Super OMEGACLAD® K-type have nearly such tolerances.
What makes this different from what you found on Amazon is the build quality and materials for the probe sheathing (high temperature probes use mineral insulation), conductors (not the chromel/alumel alloy, but the electrical connections to it), and probe length.
Consider an analogy. Let's say you found a very basic definition of automobile:
While this may be true, an inexpensive Honda Civic tops out at 209 km/h (ref). You'd need a Bugatti Veyron Super Sport to reach that upper limit (ref). What's the difference between a Honda Civic and a Bugatti Veyron Super Sport (other than about 2.4 million US dollars)? They both use combustion engine technology, but with radically different quality components.
* EEVBlog has a basic video tutorial on how thermocouples work.