HP Spectre x360 Convertible overheats, BSODs and (temporarily) unable to detect hard drive

[RaenUE]

Some background:

I had purchased a HP Spectre x360 Convertible 13-ac0XX in late 2017, and since day 1 it has had issues with regulating its temperature, where it becomes very hot in the region near the hinge (directly above the keyboard) through normal use (web browsing, etc.). This is a well documented phenomenon with this family of laptops so I can only assume that it's intended behavior; whichever engineers designed it decided to sacrifice a decent cooling system in favor of a more lightweight and thinner product.

Around the start of this year, the battery took a sudden turn for the worse, going from being able to hold 100% of a charge to only being able to hold up to what's displayed as ~65% of a charge (sometimes as high as 79%, sometimes as low as 40%) and drains far faster than it used to; this seems to be tied to both the age of the battery and it being damaged directly by the extraordinarily poor thermal regulation of this laptop. For whatever reason HP's battery recalibration utility that is reached by interrupting the normal boot sequence (I think you hold F2?) isn't compatible with my device, so while plugged in it just reaches whatever it feels like the maximum capacity is going to be today and tries to overcharge it, leading to even more heat being pumped into a system unequipped to handle it.

My current problem, which started two days ago, goes as follows:

I'm using the laptop, and it gets very hot. It starts to crash (audio stutters, programs become unresponsive) over the course of a few seconds, and then it actually crashes. The windows 'blue screen' appears for a few frames (nowhere near long enough for me to be able to see whatever it says aside from the large 😞 emote), and after appearing to automatically reboot, the following message appears:

Boot Device Not Found

Please install an operating system on your hard disk.

Hard Disk - (3FO)

F2     System Diagnostics

Pressing F2 leads to a utility (different from the one accessed by holding F2(?) during boot) that allows you to run a few tests on the system ("HP PC Hardware Diagnostics UEFI"). While running the other tests don't report anything out of the ordinary, running the hard drive test returns the following result almost immediately:

No hard drive installed. Please check that the power and data cables are connected correctly.

After some time has passed, attempting to reboot will allow the system to boot normally, though sometimes it crashes again during the boot process.

It's done this 6 times in the past 24 hours.

As far as I can tell, this is an issue with the system overheating (both due to the computer itself and the rising temperatures as we enter the summer months), which interferes with the hard drive (a SSD, which is a component that's also vulnerable to excessive heat), which causes a crash.

I've updated whatever drivers I could find, I've updated Windows 10 itself, I've tried installing HP Coolsense (it's not compatible with my device), I've tried cleaning out the vents, I've started using my air conditioner earlier than I intended to, and these crashes continue to occur. Is there anything else that I can try aside from replacing parts that'll inevitably be destroyed again by the exact same problems?