Crafting, alchemist's supplies, and proficiency checks [5e]

Both the 5th edition PHB and DMG state that proficiency with tools allows one to add their proficiency bonus when using the tools, yet there are no rules given for applying DCs to tasks with the tools or rolls made with tools. In the Player's Handbook, crafting itself is described as a downtime activity (page 187). For every day spent crafting, one or more items worth 5 gold can be crafted per day but half of the market value must be spent as investment. If something costs more than 5 gold, then you make 5 gold of progress per day spent crafting. A vial of acid costs 25 gold so it takes 5 days to make it. A suit of plate armor costs 1500 gold so it takes 300 days to make it.

This is according to the rules in the 5e Player's Handbook, and not according to reality.

In reality it takes about 2 days to make acid, and a suit of armor could probably be made in a few weeks. These rules seem arbitrarily time consuming to me. One hour per gold piece market value of the item to be produced sounds better to me. Half of the market value must still be invested in making the item, and a minimum of one gold piece must be spent (acid takes 25 hours to make and costs 12 gold and 5 silver to make, this includes the cost of a vial to put it in; candles take 1 hour to make and the alchemist makes 100 of them at a cost of 5 silver). Time is invested consecutively and the project is ruined if the alchemist is taken away from the project, though the crafter can still sleep and those hours count towards the investment of time to make the item.

There is also very little information about how to use the different tools that many characters receive proficiency with, and that's only if there happens to be any information at all (page 154).

Alchemist's Supplies is one of those toolkits that has, literally, no information. For 50 gold pieces you get a collection of gear that weighs 5 pounds and presumably allows you to make stuff if you have the right ingredients. In my personal quest to find rules for these tools I instead ended up absorbing information from the books to inform the creation of my own rules.

In the PHB, under equipment in chapter 5 (page 150), there are items that seem like they could have been made by an alchemist listed as purchasable:

Acid, does 2d6 damage, costs 25 gp/vial
Alchemist's fire, set something on fire, 1d4 damage/round, costs 50 gp/flask
Antitoxin, gives advantage on poison saves, costs 50 gp/vial
Candles, cost 1 cp each (its just hot wax but you could make wax that has a scent or wax that releases poison gas)
Ink, costs 10 gp/ounce
Oil, can set somebody on fire (5 damage for 2 rounds), presumably also keeps a lantern lit, costs 1sp/flask
Perfume, smells nice, costs 5 gp/vial
Soap, keeps you clean, costs 2 cp/bar

All of this seems a little weird, like different people wrote these items up. The biggest bang for your buck is clearly acid, as alchemist's fire is twice as expensive as acid and it gives a minimal boost of damage that can easily be saved against. Well, whatever! I'm not here to rewrite everything in the Player's Fucking Handbook! I simply want somebody to be able to make stuff using alchemist's supplies.
Alchemist's Supplies. Anyone with proficiency can use alchemist's supplies to craft any of the following items: acid, alchemist's fire, antitoxin, candles, ink, oil, perfume, soap; any kind of process that might require distillation (liqour) or calcination (the creation of oxides) can also be performed with alchemist's supplies. Proficiency checks are only made whenever the alchemist wishes to study a new substance or plant. Typical DCs are between 10 and 20, but magical substances that are studied would have a DC of 25 to correctly distill and analyze without spoiling the substance or blowing up the alchemist.

Why isn't Poison on this list?
Because there's a Poisoner's Kit listed amongst the available tools. For completeness let's look at the stats for basic poison:
Poison (basic), coat a weapon with it and it does +1d4 damage, costs 100 gp/vial
And against that, acid still stacks up as the best purchase.

The PHB actually gives a write-up for the poisoner's kit (page 154), but all it says is that it "lets you add your proficiency bonus to any ability checks you make to craft or use poisons." So, to use poisons. The DMG doesn't give any specifics about crafting (page 258) but says you can use the crafting rules in the PHB.

So here's how I would fix that:
Poisoner's Kit. Anyone with proficiency in this tool can craft poison as per the crafting rules. Any poison listed in the DMG (page 257) can be crafted with a poisoner's kit and the gold piece investment required to craft a poison is half of the market value listed for the poison. Carrion Crawler Mucus, Purple Worm Poison, Serpent Venom, and Wyvern Poison are the only exceptions that do not require a gold investment, instead these poisons require harvesting from a dead or incapacitated creature.

Re: Harvesting
The DMG states that you use proficiency with Nature or a Poisoner's Kit, but I would allow these proficiency bonuses to stack.