Vellan's page

i offer my suggestion.
there is a trait that in this particular case could be used to justify your request to your Dm its both limited and reasonable.

Empyreal Pantheon
Source Distant Shores pg. 23
Category Basic (Faith)
Your faith in the empyreal lords accommodates numerous gods, and you are gifted at adapting their wide variety of focuses and lessons to your own life. Select either the law or chaos alignment descriptor. You may cast spells with that descriptor, even if your alignment or that of your god would normally not allow it. Doing so applies the good descriptor to the spell if it does not already apply.

best of luck to your games and remember its a social game negotiation is appart of it :)

this looks like a case of negotiation.

IF (a big if I know) your DM is willing to work with ya. you can make the other prestige classes work

I have found if your willing to "Pay" a suitable price to get what ya want.

Here is how I would do so is make your case.

Hey DM nearly all Prestige don't work with the witch. None allow even 1/2 hex progression. Would you be willing to allow me to use a home brew feat like this.

(using Using shaping focus its base)
https://www.aonprd.com/FeatDisplay.aspx?ItemName=Shaping%20Focus

Hex Focus
Your powers of hexcraft outstrip your dabbling in the other pursuits.

Prerequisites: Hex class feature, Knowledge (planes) 5 ranks.

Benefit: If you are a multiclass witch, your hex abilities is calculated as though your 4 level were four higher, to a maximum level equal to your character level.

Special: This feat has no effect if you are not a multiclassed witch.

this argument while not a 100% fix for the problem a least offers some utility. and if your only going into your prestige class for a dip of 4 levels.(better then nothing.)

I have an idea that could be plausible, provided that your Game Master is accommodating and you're using Variant Multiclassing to develop as a wizard. This approach grants access to an array of wizard abilities.

Imagine investing time in role-playing the learning journey of becoming a VMC wizard and enrolling in a magical institution, like the Wizard College in the Inner Seas Magic. In my experience, most GMs are amenable to such character development if players are ready to incur significant costs. For instance, by choosing Variant Multiclassing and relinquishing half of your feats, the GM might permit the learning of wizard spells.

I would self-impose a restriction: only spells from the selected school can be learned at the standard cost. Spells from other schools would be treated as if they were from opposition schools, costing double and likely requiring two slots.

The rationale behind this is that a Witch undergoing VSM to become a wizard is, in a roundabout way, a wizard. This transformation and the associated limitations introduce an exciting dynamic to character progression and gameplay.

Is there a way to gain an arcane discovery through feats, similarly to how one can gain a sorcerer bloodline powers?

there is only one way to gain this without becoming a wizard proper. you must convince your gm to allow variant multi classing.

the long and short of it is that you give up half of your feat progression to get it as a non-wizard.

here is the basics.
your 3, 7, 11, 15, and 17 feats are consumed to use the variant multi classing. at 15th level you can select 1 arcane discovery using your character level as your wizard level for perquisites.

note this multi classing system can co-exist with standard multi classing but you can't ever take the class you took as your secondary class.(ergo wizard)

you gain a whole host of abilities themed wizard abilities ad lesser power that a normal wizard would. but it's intended to bolster the main classes spell casting. see link for full reference details.
I wish you luck in your please respond on how it goes with negotiations. :)
https://aonprd.com/Rules.aspx?Name=Variant%20Multiclassing&Category=Pat hfinder%20Unchained