There is little that character can do IC to increase the odds of personally crafting that item other than gathering sufficient duplicate ingredients to be able to make multiple attempts.
Then you have someone else do it if you can't do it yourself or won't be pleased with your success (if any).
Look, I wanted a new desk for my computer. I designed it in my CAD software, and spected out the materials, and my dad and I made a weekend project of it. Is it serviceable? Absolutely, but it is hardly great, and no where on par to be "enchanted". But that is what a PC is doing. If magic is super common in your game, then dismiss the checks (like everything in 5E, you don't
have to use a rule...), but in my games magic items are rare, mysterious, and challenging to make more of. I
don't want it to be easy or automatic. Period.
5E is geared for rapid advancement and questing. It is not a logistic game where you build an empire etc. by design--it is more fast paced. Now, it has
some downtime rules, but many groups IME don't have much downtime anyway--they want to get to the next adventure. That's fine, but you can always allow a skill to be learned either via downtime or as a reward (right there in the DM, btw for people who missed it, pg. 231):
So, if a PC wants to make magic items (and assuming they want to actually do it themselves), there are ways to do it and acquire the skills needed.
Anyway, I've already shown the checks
are not hard. Anyone with a base amount of ability and proficiency will succeed far more often than not. Throw in higher numbers and it becomes virtually academic to even bother checking.
Here's a possible solution: include optional additional steps in the construction process to decrease the DC of the checks. If those steps are disproportately costly or inefficient (in time, money, opportunity cost, etc.) they don't detract from the usual route of making the item, but do allow characters to take actions in the game world to address the challenge provided by the required checks.
It isn't a bad idea, but it's more work and an additional level of complexity that I don't want to develop or believe is even needed. If I finish the project and make it available to the public, DMs can always add more stuff on their own if they want (or remove the need for checks entirely

).