HP are an Abstraction
First, remember that HP are not just a pure measure of how much physical injury a creature can take before being reduced to chunky salsa. It is an abstraction of the creature's ability to avoid death. If a Fighter hits a Goblin for 20% of its total HP, that doesn't mean the Goblin's left leg was cut off or disabled. It means the Goblin twisted out of the way, taking a light cut to its arm and tweaking its leg. It is hurt and distracted, but not sufficiently injured to impede its ability to fight.
Similarly, the 6d10 force damage for a botched potion mix does not necessarily equate sitting on a brick of C4 as it goes off. Even though the damage is typed 'force' for the purposes of resistances and weakness, some of the actual 'damage' might be the headache, fuzzy vision, and ringing ears from the explosion. So the reason taking the explosion inside still does the same damage is because the abstraction shifts. Even though the PC is hurt more by the explosion inside, they don't see or hear the explosion so no fuzzy vision or ringing ears.
Does it even Work?
Arguably, mixing two potions in your stomach would not even cause this. It is not just the mixing of the ingredients that causes this, but the magic they contain. When you drink a potion, the magic is immediately imparted on you. You do not have to digest the potion first. So the magic is gone and you are left with a non-poisonous beverage. So by the time you drink the second potion, the two magics aren't mixing and there is no more harm than having any two or three or seven buff spells cast on you at the same time.
You might counter, what if the person drinks both potions at the same time? RAW says they can't. Even if a class ability or feat allows them to drink two potions in a single action, presumably they are still being chugged quickly but separately. In fact, if the class ability/feat does not specifically say this is an option, that would tend to be a strong indicator it is not.
What's good for the goose...
If you decide to rule that drinking two potions together results in a mixing scenario, and that the 6d10 damage result is instant death for the imbiber, be ready for the players to use it against you. Watch as they pour dozens of potions down a sleeping dragon's throat until one pair mixes badly, instantly killing it. Marvel as they slip potions into a wine tasting event to gorily kill the king and his court.
The Alchemist feat does not apply the Artificer's healing draught.
The Alchemist feats says:
Over the course of any short rest, you can temporarily improve the potency of one potion of healing...
It only works with the specifically named potion of healing magic item, which the Artificer's healing draught is not.
Best Answer
Variant: Mixing Potions is already an optional rule, so it is entirely up to the DM.
It is already up to the DM to decide if they want the Potion Miscibility table to apply to mixing potions. The artificer's elixirs seem to behave very similarly to potions, so a DM could reasonably rule that Potion Miscibility applies to the elixirs as well if they have already decided to use these optional rules for traditional potions.