You don’t need perfect reprocessing skills to perfectly reprocess - in my alliance there are multiple people with perfect reprocessing skills that can do the reprocessing for you, for a small fee. And I guess most other corporations/alliances have such people as well.
That said, if you do want to get those reprocessing skills youself, it’s not much different from training other skills.
Remap helps (which you already did); implants will help, either +4s or +5s if you’re willing to pay a lot more for a little extra; injectors are a good option if you’re not yet into heavy injected diminishing returns; cerebral accelerators (possibly with the implant that boosts their duration) are a good alternative if you’ve got injector diminishing returns and have biology 5.
Both cerebral accelerators and injectors can be bought with ISK, which means that if you want to speed up the training time you could use a decent ISK income. Just be careful that you don’t burn yourself out grinding for ISK as it’s going to take a long time.
Best way to do it is to put it all in your skill queue of your reprocessing/mining alt and then wait a year, or whatever time is needed to train it all. Start with the more useful ones for your part of space and start getting them all to level 3 or 4 for the mining improvements they offer.
(I mentioned training it on a mining/reprocessing alt, as all of the reprocessing skills are kind of useless for any other type of character as they don’t carry over to any other activity apart from mining.)
There is also a reprocessing implant that you want to have.